It takes roughly two months of being taken on a different walking tour of The Splendors of Erebor every single day for Bilbo to work out that Thorin and Company are trying to convince him not to leave. He's rather upset, of course, though it's more about the deception than the intent behind it. He tells Thorin so, very loudly and after bursting in on a council meeting, but even among the Council pretty much everyone knows the Hobbit's continued presence in the city is a matter of great importance to the King Under the Mountain, so none of them comment when the meeting is put to an abrupt end by Thorin whisking a still-complaining Bilbo away to a private audience chamber, surreptitiously signaling to anyone who would meet his eye for the rest of the Original Company to be rounded up and brought in as back-up as quickly as it could be done.
In the end it is only by all thirteen of them ganging up on him with fake tears and pretend blubbering and some impressively vague and long-winded explanations from Thorin that they convince him to stay for another month.
He spends most of that month becoming intimately acquainted with every single truly impressive treasure Erebor boasts, and a large number of the less impressive ones, as well as many of the Dwarves that have come to live there since the death of Smaug. He likes this part best, wandering aimlessly around a place where everyone knows his name and everyone wants to shake his hand, and he enjoys finding out about where they came from, and how they got here, and what they're doing now. Eventually the Original Company figure out that this is his favorite part, and then Fili and Kili come up with the ingeniously clever and supremely unfair strategy of turning up to see Bilbo with loads of little Dwarflings in tow, all of whom want to hear his stories and climb his arms and braid his hair, which he keeps meaning to have cut but somehow never seems to find the time.
Some days he goes down to Laketown (or rather, he is escorted down to Laketown by at least two of the Original Company like a flight risk) and visits Bard. He would like to go and visit the Elves, but that seems to be slightly more impossible than getting a moment alone to pack.
After the month is over there seem to be an endless supply of reasons he mustn't leave just yet. The weather isn't right. The perfect combination of supplies cannot be gathered. There is an obscure Dwarvish holiday coming up and he must be there to celebrate it. His birthday is coming soon, and they won't allow him to spend such an important day on the road. They manage to kill the most time trying to work out what his share of the treasure should consist of. The correct ratio of gold to silver to precious stones seems to be a subject of endless debate, whether it should be mostly sentimental memorabilia or spendable money splits the company down the middle, and a new method of transporting it all back to the Shire must be concocted every day.
Bilbo brings a good deal of it down on himself when they notice that he seems to be collecting a lot of the malformed, misshapen trinket jewelry that young Dwarves make when they are first learning how to shape metal. He mentions that they would make good presents for Hobbit children, as they are nice enough to be pretty but not well-made enough to give potential robbers and thieves any reason to believe the wearer has anything worth taking, and suddenly Erebor is being turned upside-down in a massive hunt for all the Training Trinkets that can be found. In the end they unearth three enormous chests full, and when Bilbo points out that he hasn't nearly enough use for all of it they simply begin the weeks-long task of sifting through every last necklace, bracelet, anklet, ring, earring and broach for the best ones of the lot.
They even, at one point, go so far as to stage a pretend cave-in at the front entrance, which isn't very convincing and doesn't work very well as a stalling tactic since he already knows where the side door is located.
Bilbo makes his first and only escape attempt by said side door at midnight on the full moon during the fourth month. It take Fili, Kili, Ori and Gimli roughly a day to catch up with him, and roughly five minutes for the four professional pouters to convince him to let them drag him back to the mountain by his coat tails. Thorin makes a great show of scolding them all for bothering Bilbo (though not, he notices, for bringing him "home" as Thorin keeps calling it) which is ruined completely by the proud, fatherly grin he cannot seem to wipe off his face.
At last Bilbo comes to the conclusion that unaided resistance is futile, and decides to wait for Gandalf.
Thorin and Company, if nothing else, are very persuasive, and they manage to keep Gandalf away for nearly half a year. Bilbo spends most of this time either dragging his friends out of the ground to explore the nearby countryside, or teaching young Dwarflings how to pick pockets and steal cooling pies without getting caught or burning their hands. He also explores the smaller and less splendid tunnels with Fili and Kili and Gimli, as none of them were raised in Erebor and so it is as much an adventure for them as it is for him. There are a few incidents with tunnels that lead nowhere, or to cave-ins, and bits of floor giving way to great chasms in poorly lit passageways, but otherwise they all have a marvelous time. It is only after ten months in Erebor, when Bilbo has very nearly resigned himself to staying there forever, that Gandalf finally returns, with perhaps the only news that could have moved Thorin and Company to consider Bilbo's need to return home.
Drogo Baggins, a cousin of Bilbo's, had died along with his wife in a boating accident, leaving their twelve-year-old son Frodo an orphan. Such tragedy is exceedingly rare among Hobbits, as they almost never put themselves into any kind of danger, but it also means that there is very little by way of established customs for dealing with orphans. Frodo is sure to be mostly swept under the rug in Brandy Hall, and whatever inheritance his spendthrift parents have left him will most likely be squandered by whoever can get their hands on it before he has the chance to claim it. Bilbo remembers Frodo as a very young child; a tiny, smiling, care-free little thing, as most young Hobbits are. Thinking of Frodo alone among distant relations in the Shire makes Bilbo's heart ache for the poor lad, but thinking of the Shire itself make his heart ache even more. What little countryside there is surrounding Erebor is simply not as green as that in Hobbiton, and he thinks ever more fondly of his own little Hobbit hole which he had left in such a hurry, always expecting to get back to, never expecting to be kept from.
He leaves two days later, with one chest of gift-trinkets, one chest of more spendable gold than he could ever need, and the heart-felt if tearful well-wishes of Thorin and Company. Fili, Kili and Gimli had followed him as far as they could without running the risk of being stuck outside at nightfall, Ori had soaked all his knitwear crying into it, and Thorin himself had hugged Bilbo close to his chest, whispering of his ever-lasting despair that they might never meet again. It is Thorin that Bilbo finds hardest of all to leave behind, and Thorin's parting words stay stubbornly with him; the soft murmurs of how he didn't fear forgetting the Hobbit's face so much as being forever haunted by it, and how he wished he could just keep Bilbo forever like one of Erebor's many splendid treasures.
The journey home is long and filled with worry. Counting days is no way to travel from the Far East to the West Near the Sea, but Bilbo cannot help but think that each day he spends on the road Frodo is alone, being given whatever is left over by parents who must naturally put their own children first, and being quite starved for the unconditional love of someone to whom you are the whole world, the sun, the moon, the stars, every spring flower and all the music of the wind as it whispers its strange tunes through the trees. He knows he is perhaps exaggerating the treatment Frodo is getting in Brandy Hall, among people he has most likely known his whole life, as brief as it has been thus far, but being surrounded by benevolent acquaintances cannot compare to having a protector of one's own, so each day Bilbo begs Gandalf to press forward just a little longer, just a little faster, just a little more. Gandalf smiles knowingly and let's Bilbo set the pace he chooses, without of course abusing the poor ponies.
They have more of a chance to stop in Rivendell than they did going the other way, and this Bilbo is grateful for. He had longed to witness the majesty of the Elves, ever since he was a small child, and to hear their songs and join in their dances, and to be told their great stories. He has a chance for all of this, and he is named Elf-Friend here just as he was in Mirkwood, but the same pull of home that tugged Thorin and Company swiftly onward from Rivendell is present in Bilbo now, and though he and Gandalf stay longer than they did with the Company, they still do not stay long.
Gandalf, on his last visit to the Shire, thankfully put some shred of decency, or at least the fear of magic, into Bilbo's relations, so he finds Bag End much as he left it. The mantelpiece and just about everything else is in dire need of dusting, but thankfully the larder was cleaned out shortly before he left, so there is nothing spoiled within it. The ashes in the grate are very old, and some of his pipe weed has gone off, but it's a matter of relative ease to throw these out along with the few weeds he finds his ever-loyal gardener, blessed old Gaffer Gamgee, has left when he continued to care for the garden without pay. Bilbo spends nearly an hour sifting through his box of gifts for a beautiful if slightly uneven ring to give Gaffer, and a flower pendant whose somewhat bent and mismatched leaves make it look all the more like a real flower for the dear hobbit's son, little Samwise.
The first thing he does as soon as he determines that his house is livable is set off immediately for Buckland to collect Frodo. At first Frodo is a bit confused as to what is happening, but he remembers Bilbo fondly, and his situation is very much as Bilbo feared; penniless and without a proper guardian to look out for his interests, though certainly not being allowed to starve or live in a cupboard. He brings Frodo back to Bag End, cooks a rather large Elevensies for the two of them, and suddenly his little Hobbit hole is beginning to feel like home once more.
The spring of his return fades into his first summer back at home, and then into the autumn reminder that the Shire is not eternally green, no matter what tricks his memory played on him. Tiny little Frodo shoots up like a dandelion in the sun, and he makes many friends among his cousins, particularly Bilbo's Took nieces and nephews, who are mostly the ones allowed to come 'round to the house of "Mad Old Mr. Baggins." He dispenses among them the Dwarvish jewelry, and watches with a vain sort of smugness as they become the greatest symbol of wealth in all the Shire, commonly referred to as Took Trinkets or Took Treasures. Bilbo discovers that there is nothing more gratifying than drawing a little Hobbitling to the still mostly full chest from Erebor, making a show of rummaging around in it before pulling out a necklace or bracelet or ring, holding it up to the sunlight streaming in through the window so that it looks like the world's most precious treasure and then lowering it slowly into the little one's reverently cupped hands. Seeing their expressions as they marvel at the trinkets is the greatest kind of magic Bilbo can imagine.
If he thinks of the Dwarves it is always a contemplation of fond memories, as the care of Frodo and the entertainment of the constant stream of other children parading through the house leave him very little time for wistful wishing to be with friends again, however dear. If he thinks of Thorin more often then the others it is only because Thorin has always been the face of the company and so is a representation of them all, and for no other reason. It is certainly not because he misses Thorin most of all.
He doesn't give Fili and Kili much thought until Frodo disappears, but it's not long after that he realizes the whole affair smacks of the two of them. With Gimli along, of course, just to make them feel young and reckless enough to think of something like inviting a Hobbitling not even into his tweens to go on an adventure all the way to the Lonely Mountain. He supposes that Erebor will not really be home for Fili and Kili for a long time, and perhaps will never be home for Gimli. They were all raised barely a two-week journey from the Shire, all Children of the Kindly West, like Bilbo. Indeed once he has the time to think about it he can hardly blame them for wanting another adventure, or for thinking that the Shire might be a good place to begin, but as he is donning his mithril mail shirt and lashing Sting to his thigh he can hardly think of anything beyond the immediate danger to Frodo, and what fools Dwarves are. Frodo must have been twice as far from home as he'd ever been before he was sure that Fili and Kili were entirely serious, and he hadn't gone back to retrieve any supplies, leaving in as much of an unprepared rush as Bilbo had before him all those years ago.
There is something poetic in that, Bilbo's Tookish side points out, but both halves of the hobbit's blood are a bit too focused on making sure that Frodo is safe to dwell on such things.
Bilbo manages to catch up with them in about a month. Frodo is, after all, still a child, and naturally prone to spending most of his time with friends, so the insistence of Frodo's two cousins Pippin and Merry that Frodo is at first spending some time staying in Brandy Hall, then wandering aimlessly about Tookland manage to delay Bilbo's departure for over a week. The Dwarves, however, are hindered by not being able to press a young Hobbitling too far too fast, and Bilbo can set his own pace, riding hard throughout the day or long into the night. By fortune of an ambiguous nature, however, the entire race is brought to a screeching halt when Fili, Kili and Gimli, with Bilbo not a day behind them, run into the Company of Royal Guards, Erebor Ambassadors, one very agitated Gloin, and Thorin, King Under the Mountain.
It is difficult to say whether the importance of retrieving his errant heirs or his own desire to see this part of the world and all the treasures he had overlooked within it was what had prompted Thorin to place Balin in command of his city and set out on this quest himself, but with one look at Bilbo he forgets all about his wayward nephews and the stern lecture he is giving them. He sweeps Bilbo up, takes the Hobbit off his feet and holds him tight as though trying very hard to just absorb Bilbo into his chest.
After being tactfully informed by Fili that if he is trying to devour Bilbo he's doing it wrong, Thorin sets Bilbo back on his bare feet and apologizes, not only for his own behavior but for that of his nephews. Bilbo cannot deny the worry he has been to, but neither can he bring himself to try and convince Thorin to be any more sorry for it than he already is. Fili, Kili and Gimli, having been discovered on their way back to Erebor instead of farther from it, are no longer a worry, so Thorin and Bilbo are free to seclude themselves somewhat to talk.
Bilbo shows Thorin the inscription he has had inlaid into Sting.
Thorin tells Bilbo of the gardens that have sprung up in and around Erebor, tended by the admittedly inexperienced hands of the Dwarves who heard Bilbo tell of his own little garden in the Shire.
Bilbo does not ask if Thorin encouraged this, and Thorin does not volunteer the information.
He does volunteer that there is no Queen Under the Mountain, nor any Consort to the King, as of yet. He volunteers that he doubts there ever will be, that no companion can compare to the one that he knew on the road. The one who defended him and his Company, all the subjects he had, through every terrible trial. The one who was quick and clever, who stole all the prisoners from the Elf King's dungeon right out from under his nose, and who charmed a dragon into showing it's weakness. The one who he will never forget, for that face will haunt him ever more.
At some point Frodo steps on a twig, giving away his hiding spot behind a nearby tree.
Bilbo immediately turns all attention to his charge, and is surprised when Thorin does the same. Thorin asks what Frodo knows of his Kingdom, and the little Hobbitling dutifully recites the list of the Splendors of Erebor, which Bilbo knows by heart. When Thorin wonders if Frodo really knows what any of what he is describing is meant to look like Frodo produces the Took Trinket that he wears everywhere; a simple medallion etched with a slightly crooked but beautifully detailed flower.
Frodo is rather surprised to learn that he is addressing the King Under the Mountain. He is even more surprised when he is told that if he so wished it, he might become a Prince Under the Mountain. Indeed, Thorin would like that very much.
Bilbo is very sure Thorin is not serious.
Thorin is equally sure that he is.
It is at this point that Gandalf shows up, volunteering to deliver any messages Bilbo might have back to Hobbiton, but isn't paid much heed for a while as Bilbo is rather busy having his face speckled with loving kisses.
The journey to Erebor passes in a haze of excitement and anticipation. The party stops at Rivendell, mostly because Frodo has never seen an Elf before and desperately wants to. Thorin quickly discovers he is very weak to the demands of little Hobbitlings, particularly when Frodo demonstrates his alarming ability to open his eyes so wide Thorin can only describe it as a pair of mirrors into all that is pure and innocent in the world. Frodo is no less excited about the Elves in Mirkwood than about the Elves in Rivendell, but the darkness of the forest proves a terror that not even his boundless curiosity can stand up to, at least not at his current age. For the moment, he rather prefers the mountain.
Fili and Kili adore their new cousin, and delight in showing him every square inch of Erebor and every last treasure they described, watching his wondrous eyes flick from marvel to marvel. Ori greatly enjoys the challenge of knitting things so small, as well as the sight of the them fitting Frodo so snug. Balin is forcefully reminded of a young Dwarfling he once knew, an eager little Prince Under the Mountain completely entranced by the world around him.
Frodo, however, likes best of all what the King shows him.
The garden takes up a whole cavern, lit by crystals which glow with a strange power. It is full of the things he knows from the Shire; tulips, pansies, daffodils, petunias, lilacs, bluebells, orchids and every imaginable kind and color of wildflower. Frodo likes these best, as he'd never thought they could grow without sun and wind and wide open spaces, but the closest he ever gets to an explanation is that Gandalf helped, which doesn't really satisfy him but he supposes is reasonable enough. Thorin spends almost as much time helping Bilbo tend the flowers as he does admiring his gold. Bilbo lets his hair grow long so that Thorin and Fili and Kili and any little Dwarflings who want to can braid beads into it.
In the end Bilbo and Frodo develop a little saying between them, which seem to sum up their lives quite nicely.
Happiness cannot be bought; it must be grown.