Concering Bilbo Bagginses...

[lathspell]

I don't think the new editions of The Hobbit are revised. But maybe someone with an old edition of the book can help us out in this one.
In my opinion Gandalf clearly points out why Bilbo gives another account than the true story. When he tells Bilbo about the story of the Ring, and the making of the Rings of Power, he tells Bilbo this:

... Then I heard Bilbo's strange story of how he had "won" it, and I could not believe it. When I at last got the truth out of him, I saw at once that he had been trying to put his claim on the ring beyond doubt. Much like Gollum with his "birthday present". The lies were too much alike for my comfort. Clearly the ring had an unwholesome power that set to work on its keeper at once...

This little part of that tale makes quiet clear that it wasn't Bilbo changing the story because HE wanted too, but because the Ring made him change the story. I think Gandalf is right in the last part too (about the Ring having an unwholesome power that set to work inmediately), because Bilbo didn't tell Gollum either. Why wouldn't he? He didn't know that the Ring belonged to Gollum before he found it. And it took a long before he guessed that it might have been so, only after Gollum begins to whisper to himself.
I guess it's the same "power" that makes Bilbo change the story, as maked Smeagol kill Deagol. Afterwards the birthday present-story was easy to make up for it was his birthday, but this also he made up under the domination of the Ring.

So, in short, Bilbo had nothing (or a little) left of his own free will in the matter concerning the Ring. The Ring had the greater power as he had with all its bearers except Sauron himself.