I've tried w/o success to take a bear with a bow when I lived in CA. I had a buddy who got a few over the years with a bow. I would always joke that I was not going to hunt with him, he was smaller and faster than me! I was going with "Sam" who weighed about 300 lbs and was real slow. If I'm going to get chased I want to be faster than my hunting partner!
Seriously though, my sucessful buddy said that the bears he had hit had run away (opposite direction) after struck with the arrow. He was always well camo'd and hidden from the bear. Not sure what a bear would do if he saw who just hit him though.