Something you need to keep in mind is there is a big difference between hunting an animal and killing one in self defense. You can hunt a bear with a bow, but I would not try to defend myself with one. When hunting the goal is that the animal doesn't know you are there and is not alerted. He is going about his/her business and suddenly gets shot. Normally running away and expiring.
That is a HUGE difference between a large dangerous animal that knows you are there and considers you a threat to itself or offspring. Especially an animal that is as fast, strong and smart as a bear. These are one of the few animals that can hunt you back

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Like I have said in other posts, sure a .357 or other pistol will kill a bear, but if you think it will reliably stop a charging bear in it's tracks or drop it in a few yards you will probably lose that bet. I still say save at least one shot so you don't have to die while the bear is eating you alive (which they do).
The simple thing to do is if you are this worried about being attacked by a bear, just don't put yourself in that situation. I have this phobia about sharks. They fascinate me, but scare the crap out of me at the same time. I have this deal with them, I will stay out of their back yard if they stay out of mine

. It is pretty simple really, I don't want to be eaten by a shark, so I don't go swimming where sharks are. Not go swimming where sharks are but take a poison tipped spear gun with me hoping it will save my life.
That last paragraph was a joke, but it does make a good point.
Paul