When Frodo brings the one ring of power to the Last Homely House East of the Sea at the request of Gandalf, the council who are summoned there at Rivendell are thrust into a terrible and difficult choice. Now that the ring has surfaced, they have no choice but to try to destroy this dark object. But this can only be done in the fire of Mount Doom, where the ring was forged. So the difficult decision lies before them of how to achieve this impossible task, and who to send as the Ring-bearer. Sometimes, within these stories, someone must be sent on an impossible quest, despite knowing the danger, and despite the fact that in all likelihood, they will never return.
This is because the ring will stop at nothing to get back to Sauron, and he will stop at nothing to find it. As Aragorn points out, no one else can wield it: “it has no other master.” The ring is cunning and deceptive. It is capable of absolute betrayal and treachery, including manipulating those around it, drawing them in, using them to commit heinous acts and then tossing them aside in favor of another who will get them one step closer to Sauron. This is shown countless times across The Hobbit and the Lord of the Rings movie adaptations as well as the original books. It abandons Gollum in the tunnels below the goblin caves; it abandons Isildur in the river as he tries to swim away from the orc attack. But if the ring is so good at escaping its wearer in order to get back to its true master, why didn’t it escape Bilbo in the 60 years between the quest for Erebor and the War of the Ring?
There are three main reasons why this is the case. The first is that Bilbo is a hobbit, and as such, is particularly difficult to manipulate or corrupt. Hobbits have a natural resistance to the influence of the ring, because they are fully content in their simple lives and have no desires for power or war. Bilbo in particular had already seen more war and devastation in the past few years than most men would experience in decades. He would have done anything possible to avoid more battles, more destruction, more cruelty. Therefore, it was near impossible for the ring to be able to twist him into making a foolish mistake and revealing its existence, so it stayed hidden in Bilbo’s pocket for the better part of those 60 years.
Even so, the Ring did eventually start to take its toll on the old hobbit. By the start of the Lord of the Rings, Bilbo is feeling old and worn, paranoid, aggravated, and none too friendly. The ring has been slowly wearing him down, gnawing into his mind and body, but it has taken long years to be able to scratch his hobbit immunity to its allure.
The second is related to the first, in the sense that because it was so difficult to corrupt Bilbo, the opportunity to betray him didn’t present itself. Bilbo spent most of that time within the Shire, and most of that time by himself, and so the ring never had a chance to jump ship in favor of someone who would bring it closer to Sauron. Although Bilbo did have visits with the elves in the woods, and the odd dwarf in his pantry from time to time, he was always careful to keep the ring locked away somewhere safe. Although he didn’t understand the full extent of the ring’s malice, he did know that he wouldn’t want to part with it, or for it to be discovered. He didn’t even tell Gandalf of its existence, and the grey wizard is one of his dearest friends. The Ring couldn’t have escaped him within the house, and couldn’t have fallen from his pocket on the road either, because he seldom left Bag End.
The third possibility is that the one Ring of Power was biding its time. The ring is very clever after all, and is able to sense when it is in the presence of someone who it can tamper with. It is highly possible that the ring was waiting all that time, both for the right bearer to present themselves and take it back to its master, and for Sauron himself to regain enough strength and power to be able to find and wield it. This is during a time when Sauron is behind the gates of Mordor. There, he is amassing an army, recuperating his dark essence, and preparing to wage war and dominion on Middle Earth. Perhaps the ring knew that it needed only to wait, and eventually its whereabouts would be located in the Shire, and the Nazgul would be sent to retrieve it.