I don't know, that .22 might be a bit overkill for a several hundred pound black bear. I think one of these will be sufficient medicine for a black bear:
With, of course, the correct ammunition. I suggest +P hardcast
Here in Oklahoma, all we have are small black bear, mostly ones that have come over from Arkansas. When I was a kid I watched one tangle with three coon hounds of my dads, and he put a pretty good whooping on them.
I don't think I would want to use any .22 caliber on something that had the potential to eat my butt.
.22s around here are used for small game up to yote size, anything bigger requires a .30 caliber in my books.