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.
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He is scared to, the ring influences him to "protect his precious" and he likes the way prestige he gets for being so "sneaky" and "burglar like" because of using it. Therefore, if he revealed the ring, they would not be so impressed by Bilbo since the ring makes him invisible and helps him hide.
The Ring was stolen, and while they had all suffered for the trip into the goblin caves, only Bilbo came out without any trouble. In addition, it was a magic Ring that begins working on its keeper at once - the possessor would not want anyone to know about it that might take it from him.
It may have been the influence of the One Ring on his mind already.
Bilbo was recruited by Gandalf to join the dwarves' mission as a master thief. Bilbo does not tell his friends about the magic ring because he wants to earn their respect as a thief. Alternatively, it could be the ring's power already beginning to assert its influence over Biblo. In the end, however, Bilbo does tell the dwarves about the ring and that it has the ability to make him invisible, which was what enabled him to escape Gollum, the goblins, and to sneak into the dwarves' camp while Balin was on watch.
In The Hobbit, it is presented as simply a matter of Bilbo's pride. The dwarves are are finally beginning to be impressed with Bilbo as burglar and he does not want to admit that a large part of his success is due to an magical artifact and has nothing to do with his talents.
In The Lord of the Rings, the reasoning appears to be more sinister. He wants to keep the ring a secret so that his possession of it will not be threatened, so that he can keep his hold on the Ring. There is an implication that this is due to corrupting force of the One Ring immediately seizing upon Bilbo, making him develop a fixation and obsession with the ring, and inspires him to lie to make sure he can retain the ring.
There were two editions of The Hobbit that were written. Prior to the Lord of the Rings, the ring itself had no history, and so Bilbo actually did reveal that he obtained the ring from Gollum. Later, when the Ring's malevolent history was dabbled into, Tolkein realized Gollum would never give up the ring willingly, and re-wrote the chapter in later editions to reflect that Bilbo more or less stole the ring.
Canonically, Bilbo told Gandalf and the Dwarves that it was a prize for winning the riddle game. Gandalf had his suspicions, however, and managed to get the true story from Bilbo much later. The fact that Bilbo would lie about the entire incident struck Gandalf as alarming, since Hobbits weren't prone to such things as lying. One might say that the reason Bilbo lied was due to the effect that the Ring was having on him.
It is possible the Ring had already begun to affect Bilbo, and he would not want any to know what he had, and therefore try to take it from him.
They feel more safe knowing that Bilbo just saved all of their lives. And they treat him with more respect.
Because he wants the ring for himself. It is the very same ring as in LOTR. The same ring that frodo wants for himself. The same ring that bilbo tries to take from frodo.
Bilbo can see that he and the dwarves are about to be overwhelmed by the spiders and decides he has to disappear in front of them. After they get away the dwarves are bewildered by his turning invisible and must have the story of his escape from Gollum again. Balin in particular feels he is owed an explanation because Bilbo made him look bad earlier when he snuck past Balin on guard.
When? At the beginning, Gandalf the Grey chats to Bilbo saying he is looking for someone to go on an adventure. Bilbo, being timid at the start, is a little rude to Gandalf, but invites him to afternoon tea. Gandalf laughs and with his staff marks the front door "burglar for hire, etc". Later a knock on the door and after a while 13 dwarfs and Gandalf are in Bilbo's Bag End residence: Dwalin, Balin, Fili, Kili, Gloin, Oin, Ori, Nori, Dori, Bifur, Bofur, Bombur, and Thorin Oakenshield. During the adventure Bilbo is separated numerous times from the dwarfs, and aids them in their escapades with his new found confidence and bravery and his magical ring.
Smaug tells Bilbo not to trust dwarves:In return for the excellent meal [of the Company's ponies] I will give you one piece of advice for your good: don't have more to do with dwarves than you can help!Smaug-The Hobbit: "Inside Information"
The White Stripes wrote the song We're Going To Be Friends.
J.R.R Tolkien writes "Bilbo had heard tell and sing of dragon-hoards before, but the splendour, the lust, the glory of such treasure had never yet come home to him. His heart was filled and pierced with enchantment and with the desire of dwarves; and he gazed motionless, almost forgetting the frightful guardian, at the gold beyond price and count" From this we can summarize that Bilbo was absolutely taken aback from the wondrous sights he sees. J.R.R Tolkien also writes that Bilbo gazed upon the dragon and treasure "for what seemed an age" in my opinion he felt a certain thrill from this sight. Hope that helps!