At the end of the book, Bilbo says to Gandalf:
“Then the prophesies of the old songs have turned out to be true, after a fashion?”
“Of course!” said Gandalf. “And why should not they prove true? Surely you don’t disbelieve the prophesies, because you had a hand in bringing them about yourself? You don’t really suppose, do you, that all your adventures and escapes were managed by mere luck, just for your own benefit?”
This sort of summarizes my take on the nature of Bilbo’s quest. It’s not really about him, he’s sort of an instrument of fate.
There is too much luck and coincidence for it to be really accidental. The clues are meant to be deciphered, and people are meant to be in the right place at the right time. It’s a little push to make success more likely.
Tolkien, in what he said was the most important passage in LOTR, said that the wheel of the world was turned by the small hand because the greater was looking elsewhere, and this is what Bilbo is doing in his small way.
“Roads go ever, ever on” and Bilbo has gone on with the road for a way, then stepped off to a safe haven, leaving the road to others. He has grown in the process, as maybe all of us do when we manage to do what’s needed.