I am not sure I would try to use a .22 mag on a black bear... In all likelihood, you would do nothing more than piss it off. Even two legged folks, .22 mag doesn't have much knock down power. If it is coming out of a rifle barrel and you are using a semi auto where you can place multiple shots on target, them maybe...
I'm not near the firearms expert as CJ, and others, so I didn't respond to this. But wanted to. I would definitely think, if your primary reason is as a defense against bears, a .22 might just do enough to rile the bear up and put you in a more dangerous situation.
