In the cave he noticed it when he was invisible
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Initially, Bilbo wanted to go on an adventure because most hobbits have not left the Shire before. But after interacting with the dwarves throughout the journey, he soon realized that he wanted to help the dwarves reclaim their home at Erebor from the dragon Smaug the Golden.
thorins is much powerfull
He uses the ring many times in The Hobbit. He uses it to escape from Gollum and exit the mountain, he uses it when spying on the giant spiders in Mirkwood, he uses it when the Dwarves are captured by the wood elves, and he uses it when in Smaug's lair.
Gandalf believes in Bilbo, and he says in the book that he wouldn't of brought-en him if he wasn't in good use.
The dwarves had begun to think Bilbo should put on his ring and scout the front door. He was getting tired of them and their expectations of him. And finally when the key-hole was revealed none of them thought to use the key! He had to shout at Thorin to get him over to the door in time.