Is Bilbo a conventional hero? Or is he a modern sort of hero?
The conventional heroism involves both physical and emotional masculinity. Common character types that embody conventional heroism I can think of right now are: military leaders, kings or princes, or someone who exhibit strength, leadership and some unique ability that gives him an edge. Bilbo, of course, is none of those things–other than his exceptional stealth, his quiet movements and his wit.
I think Bilbo is modern in his individuality and his journey of self-discovery. Despite his reluctance, I argue that he partially accepts the adventure and yearns for it. His constant complaints about the quest for treasure (whether it be discomfort or the dwarves’ clumsiness) are perhaps a more realistic portrayal of an individual. If that is a sign of femininity than the dwarves are then equally feminine, because they complain almost just as much as Bilbo despite the bushes of manliness under their chins. After all, how can you not miss the warmth of your home after leaving it for the first time?
Through the adventure, what frequently motivates Bilbo to act is the desire to prove his worth to the dwarves–as many of them express their doubts in Gandalf’s selection of the “thief” and Bilbo’s ability as the thief. His dramatic reappearance as he takes off the ring before the band of dwarves serves to surprise his companions and to reaffirm his ability and self-worth.
It’s because he’s little and seemingly feeble that he’s driven internally to prove otherwise. His confrontation with a giant spider and his subsequent victory gives him the confidence that he needs to continue the adventure and assume a leadership role among the dwarves. Indeed, maybe he is special precisely because he is little. While others generally don’t expect much from a little guy like him, he proves to be a crucial member of the treasure-quest team as he repeatedly saves his companions from harm’s way. Even the dragon hesitates in extinguishing his existence because even though it can’t see Bilbo, it smells his alien scent as a hobbit and can’t quite make it out what he is. This possibly factors into Tolkien’s decision in placing Bilbo as the only hobbit in the team of dwarves–to emphasize his uniqueness and individuality.
Returning to the point about Bilbo being a modern sort of hero–the pursuit of individuality and self-discovery seem to be a relatively “modern” theme in literary works in general (please correct me if I am wrong). Unlike the Lord of the Rings trilogy, the large cast of characters each have their specific function within the story and cooperate/interrelate for the final events to take place. The protagonist Frodo, though also a hobbit, is not as individualized as Bilbo (from what I can remember at the moment). The story concerns the world–Middle Earth–as a whole, instead of the fates of the individual characters.
I seem to have digressed here. To briefly conclude: I think Bilbo is a modern hero uncharacterized by the conventional heroism, but is unique in his wit, stealth and his motivation to assert self-worth. His incessant complaints and obsession with domesticity do not make him effeminate, but further individualize him as a realistic and developing character as he finds his place among the dwarves.