You'll probably hear a lot of this: 'it's better than nothing'.
It is better than nothing, but bears are tough animals with very thick skulls. If a bear was on top of you, you could probably kill it point blank with a .45. But the trick is to kill it before it gets on top of you and at any distance other than a foot or two, I think the .45 is going to have a problem given that the bear will likely be facing you, presenting you only with the skull or front/chest shot, both of which are marginal kill zones with less than ideal calibers.
I like carrying a .44mag in bear country, and highly recommend picking up something in that caliber.