Because Bilbo wanted to sneak away from the camp to go see the Dale men, and he wanted to do it in secret.
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Balin goes part of the way down the tunnel with Bilbo, and Bilbo takes one single golden goblet from Smaug’s immense hoards.
He takes it upon himself to save the dwarves, multiple times (from the spiders and the elves most notably.)he was a hobbit who knew how to sneak around places without being seen
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).
Bilbo escaped from the cave in The Hobbit by using his wits and the magical ring he found earlier in the story. He put on the ring, rendering himself invisible, and slipped past Gollum, the creature guarding the exit. Bilbo then followed Gollum out of the cave and made his way back to the company of dwarves.
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.