Black bears seldom attack people even when shot/wounded by a hunter.
My personal opinion is that the 357 mag should be considered the least caliber for whitetail deer from a handgun. I tend to believe something larger works better.
For black bear, my vote is for something larger than 357 mag. I would start with 41 or 44 mag. But if you make a good shot, there is no reason why a black bear won't go down with a 158 gr JSP from a 357. The thing about black bears is that they tend to run off a ways regardless of what you shot them with unless you hit them really hard or are lucky based on what rifle hunters tell me. I have never shot a black bear, never really wanted to hunt them.