Just read an interesting account in Traditional Bowhunter magazine, Sep 2004 issue. Story of a bowhunter, Ed Bangs, who had a Brown Bear sow charge at him. He was able to kill the bear in self defense, by drawing his .357 mag and getting several shots off in the face of the bear. One of the few documented cases of a charging bear being killed in self defense by a handgun.
there was another post discussing whether a .357, .41, or .44 would work best on bears. Kind of same thing. Argument was for the .357 and .41, that you could control the getting the shots off quicker and they might actually even have more penetration.
Again the best thing for bear defense, would be a rifle in 375, 416, 45-70 or 12 guage slugs. But, if you are solo bow hunting, many will just carry a handgun as backup (where it is allowed.)