He could be hurt by a magic spell gone wrong. For instance, a wizard they encounter on their journey accidentally casts a spell on Bilbo that causes him pain and weakens him. The group then has to search for a way to reverse the spell, which could involve going on a side - quest to find a special herb or artifact. This would add an interesting twist to the typical Hobbit adventure story.
Bilbo could get hurt in a cave - in by a hidden trap. His companions would then need to figure out how to treat his wounds and get him out of the cave safely. This would create a lot of tension as they might not have all the necessary supplies with them.