I'll add my 2 cents. and comment on Lloyd's information.
From what I have read some of the best hunters that use dogs to go after mountain lions, use 22 caliber (22 Bee) handguns to shot treed cats. The idea is that the bullet goes throught the cat, that cat feels safer staying in the tree and it bleeds out up in the tree, dies, and fall to the ground. The use a 22 keeps the cat from attacking and hurting the dogs.
I would assume (assuming is very dangerous to do) that a treed bear is similar. So what is good for shooting a treed bear may not be the same as what you would use to shoot one that is on the ground.
I feel that a 357 Mag is a formidable firearm, if given the proper handloaded ammo. I have some 357 Mag hunting ammo for a Ruger Blackhawk that is well above published max loads, but was carefully worked up to and not "overpressure" in that particular revolver.
The 357 Mag has been used to hunt all kinds of things. I would also say that there are black bear and black bear. Most of the black bear I have seen in clear cuts out in Western Washington are small and not too much bigger than a very large dog. I would not have any qualms about being able to stop one of them with a 357 Magnum.
Then again, there are remote places I have been to, like parts of Alaska and the Montana Rockies, where some of the black bear get a bit bigger and stronger, that I would feel a 357 Mag is better than throwing rocks if cornered, but I wouldn't use it to go after a large bear.