Would you feel safe using a 45 ACP for protection against a Bear?
In a word, "No."
If I had nothing else and was forced to depend on a .45ACP, I'd load it with the hottest 230 gr FMJ that I could find and hope like Hell that I wouldn't need to use it. A .45 ACP 230 gr. FMJ at 850fps is good for about 26 inches of soft tissue penetration (according to the Schwartz bullet penetration model) unless you hit bone- a real problem against even small bears.
I'd much rather have at least a .44 Magnum with a 300-310 gr HCSWC at no less than 1100 fps with penetration that'd push the four foot mark.