The ring has a consciousness of its own. The ring knew that Frodo was going to take it to be destroyed, whereas the one ring abandoned Gollum as it knew that Gollum would never return it to Sauron. The ring used Bilbo as a carrier or a vector.
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There are several different theories in this regard, such as (1) that Sauron's pull on the Ring was stronger while Frodo was in possession, (2) that Frodo's intent to destroy the Ring created a greater antagonism with the Ring, (3) that Frodo's proximity to Mordor and Sauron's forces made the Ring more intent to control Frodo to take the Ring to nearby enemies.
There is also the external-to-the-books view that when Tolkien wrote "The Hobbit", he had not actually conceived of Bilbo's Ring as the "Ring of Sauron" and the mythos of the "Ring of Sauron" only developed when Tolkien was writing "Lord of the Rings".
He was so pleased by their praise at the way that he so cleverly snuck into the camp without being seen, that he decided to keep the Ring out of it for a while.
The first and primary protagonist in the Lord of the Rings is Frodo Baggins, close relative to Bilbo Baggins from The Hobbit. However, in Book 2, Tolkien splits the story into three storylines. Frodo continues as a protagonist; however, now Aragorn, Merry and Pippin are also protagonists, the story following all of their perspectives as the world of Middle-earth readies for war.
The main conflict can be seen as the struggle to get the Ring destroyed and to keep Sauron from getting it. The first volume, Fellowship of the Ring, is mostly an account of a journey, and the conflict is with obstacles between the protagonists and the destination. These obstacles include, but are not limited to: -Black Riders -An evil forest -Evil tomb spirits -More Black Riders -Bitterly cold and snowy weather -Wolves -A monster in a lake -Lots of orcs -A Balrog, a being of fire and shadow -Lots more orcs It should also be noted that there is also a less physical and more internal conflict: the struggle to resist the power of the Ring. The ring wants to get back to Sauron, and tries to poison the minds of those near it, so the protagonists must be constantly resisting its lure.
So that he could give a straight answer to his neighbors and friends when they asked him why and where he was going. It created less suspicion amongst the gossipers of Hobbiton. That way, Frodo could just set out on his journey from there, away from all the peering eyes, and creep away quietly, without causing a big scene. Merry Brandybuck helped him pick out the house.
Because during the unexpected party, Thorin promised Bilbo 1/14th payment of the treasure in return for Bilbo's services as a 'thief'. Though Bilbo did not do much in the way of being a thief, he did save the dwarves from Thranduil, as well as help them gain entrance into the mountain. They also wanted him on the journey because it would have been unlucky to take on their journey with 13 members. At the end of their adventures, Bilbo had obviously earned his 1/14th share, so Thorin fulfilled his promise and sent Bilbo home with a chest of treasure (though it is hinted later on in LotR that Bilbo ended up receiving more).