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.
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The Elves used to take him out for walks through the forest and let him climb on trees. One day he refused to come down. At the same time there was an Orc attack, and when the battle was over the Elves found Gollum's guards slain beneath the tree and Gollum gone.
He (inadvertently at first) used the ring to become invisible, and followed Gollum to the corridor leading to the exit, then snuck out past the goblin guards. At one point the ring slipped off his finger and he was visible to the goblins for a moment, but he quickly put the ring back on and they couldn't find him.
In the Hobbit Bilbo escapes from the cave because Gollum thinks that he found his ring and knew the way out.
So Gollum started to go to the exit but Bilbo had put on his ring and followed Gollum to the exit. However Gollum was blocking the exit because he was searching desperetly so Bilbo had to jump over him to escape.
Gollum noticed the wind fly past him though but he didn't manage to catch Bilbo
Gollum, believing that Bilbo already knows the way out of the cave, leads an invisible Bilbo to the exit. Gollum also believed Bilbo to have his ring (his precious), so he fervently searched for him. However, Bilbo not knowing the way out of the tunnels, indeed found freedom by following Gollum. And indeed Bilbo did have the magic ring and was able to follow Gollum undiscovered because the ring made him invisible.
While running from Gollum Bilbo trips and the great ring of power "accidentially" slips onto his finger & he escapes while invisible.
Gollum guessed that Bilbo actually knew the way out and thought he was chasing Bilbo. Bilbo just followed Gollum and found the exit.
The dwarves are Bilbo's friends for most of the Hobbit.
He proves himself useful on several occassions. He rescues them from the spiders in Mirkwood. His warning allowed Gandalf to escape and rescue them in the Goblin Cave. He gets them out of the elf dungeon in Mirkwood. And then he gets them into the Mountain.
Bilbo Baggins was hired to be the burgler in the Hobbit.
Bilbo was 50 years old in The Hobbit, which was considered middle aged for hobbits.
Yes, in chapter 9 the dwarves (but not Bilbo) were imprisoned by the Wood-elves in Mirkwood forest.