I'd feel better with my 870 Remington loaded up with Brenneke slugs. As a last resort, if you do carry a handgun of the sort that you'd use for protection against humans, those who've "done it" say you should use hard cast or FMJ. Penetration is what you want; aim for the brain and hope for the best. Few handguns will enough structural damage to stop a big bear without shutting off the CNS.
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“I'd rather have questions that cannot be answered than answers that can't be questioned.” —Richard Feynman