Here in the East, brown/grizzly bears don't exist, only black bears. With that in mind, I feel that I can get away with a .357 Magnum (non-snubby) loaded with hot LSWC or LFN, hard lead, at least 158 gr -- at a minimum. A similarly loaded .41 Mag or .44 Mag would be even better. For brown/grizzly bears out west, I wouldn't go with anything less than a .44 Mag -- .454 would be even better, again similarly loaded.
A non-expanding penetrator that would have the chance to make it through the thick, slanting skull into the brain is what I'm looking for. A hit to the brain will stop the bear right in his tracks.
Note that I'm not advocating the knife. The problems with the knife are threefold and interrelated:
1> If you are close enough to the bear to use a knife, the bear is close enough to you to use claws and teeth.
2> The bear has a whole mouthfull of teeth and 2 paws full of claws, you have 1 knife.
3> The bear is bigger and more powerful than you are.
Add to that the bear will only get madder the more you slash and has a greater circulatory capacity than a human, and you end up with the bear maybe dying later but definately killing the knife wielding human. Remember that the knife will NOT be able to reach the bear's CNS because of the heavy bone protecting it.
OTOH, a brain shot on a charging bear just might kill the bear right there, assuming that the human can get an aimed shot off and so get an instantly fatal hit. Even if the bear is in contact range, the possibility of the human making a CNS hit is still there, hence the odds -- while not all that good -- are still better for the human than if a knife was being used.