I think this novel is actually about the formation of Bilbo Baggins from comfort-loving Hobbit into a fully fledged hero at the end of the novel. Thus he doesn't start off as a hero but certainly as his character develops by the incidents that he faces he shows himself to be truly heroic, especially in contrast to other "heroic" characters. Just consider, for example, how Bilbo shows himself superior to Thorin by rejecting greed and gladly giving up his share of the treasure to deliver the Arkenstone to Bard.
I would consider Bilbo a hero, just for the fact that he steps way beyond his comfort zone and goes on a large-scale adventure. He puts himself at risk on several occasions to look after the welfare of others, and Bilbo is doggedly persistent, not giving up--even when the going gets tough!
In the archetypal sense, Bilbo is a hero. He embarks on the Hero’s Journey and does go through all of the phases. In many cases, the archetypal hero is not what we would consider heroic, at least to begin with. The hero often gets pushed along on his adventure, as Gandalf does for Bilbo. Few archetypal heroes actually go searching for the adventure or journey. The journey is a difficult and painful process, full of danger and mistakes. Bilbo makes plenty of mistakes, but in the end he does change and mature. In essence, the archetypal hero is willing to put his mission above himself. This hero is able to sacrifice his comfort (no small feat for Bilbo) and even his life to save others.
A hero also embodies a set of values to be upheld. Bilbo is timid and is a follower, but is also humble and true to his firends, and tries always to do the right thing - even when it might be unpleasant (like handing over the Arkenstone). He also embodies a good story arc: he is less timid by the end of the story, because he actually tries to be bolder. We see this when he confronts Smaug as well as the spiders in Mirkwood. And he uses his head instead of more athletic aspects of heroism, as when he rescues his friends from the Elves. So yes, I'd still call him a hero not because he is larger than life (excuse the pun), but because he is as small as we all often are, and still tries to do what is right.
I agree with post no.#6...he is a hero he risks his life many times in the book.
Why is Bilbo willing to play the riddle with Gollum?