I usually just use the shortbow. Most of the times I don't have any trouble, it's just the story quests where even if I don't attack at all the enemy will just ignore my bear and try to kill me instead. So I don't know if the weapon I'm using really has anything to do with it.
Though I'm level 19 now and have crafted a level 20 shortbow and longbow so I could switch from shortbow to longbow if I needed to.