"...but there are a few reasons Bilbo might even have chosen to tell the entire story from a point of distance. Some are more personal than others.
The very personal reasons are that bluntly Bilbo has a weird and somewhat socially awkward combination of desire for an audience and applause, along with an absolute discomfort with being seen, and particularly being seen to be anything other than composed and if necessary a little ironic.
These are things that actually continue across his character, from the moment we're first introduced to the moment we last see him: he feels things very, very deeply, and would also rather cut off his own nose than seem to take anything more seriously than, maybe, a contentious town council meeting. He will absolutely die for his friends, but will avoid the awkwardness of a long good-bye from his (let's face it) adopted son, because it's awkward.
He will be absolutely terrified but gods forbid he not have a quick comeback! That would be the worst.
Bilbo, in short, vastly prefers to be in control of how people see him. He may even be willing to make himself look silly, or allow someone to see that he's moved or upset, but he'll only be willing to do it on his terms. The tone he brings to his memoir is detached, ironic, understated and avuncular.
If you're like that, it can be much more comfortable to, for instance, write about yourself in the third person. It's one thing to say "Bilbo was very frightened" and quite another to say "I was very frightened."
Further more, we can see from the other hobbits - and Pippin discusses it specifically with Aragorn, apologizing for it only to have Aragorn essentially say yes, I know - that this is not atypical for hobbits. Hobbits overall are not comfortable articulating strong feelings; it's not Done. The more they feel the more they will take any opportunity to sidestep saying it aloud.
So it's entirely possible that it's just not done!!! for a hobbit to write a memoir from the first person. I would definitely buy that. "