I carry a 1911A1 when I go out in the woods here in KY, but I only have to deal with black bears and rabid skunks.
The most critically important detail here is that you do not deal with a grizzly bear. You can knock down a rabid skunk, handle a black bear, but if you get yourself in a situation where you're being charged by a grizzly, the vast majority of the time you'll hardly have a chance at all to draw a firearm, much less use it effectively against a charging grizzly.
This was from a very very experienced AK bowhunter, who carried a 1911A1 with him in Alaska. If there is a confrontation with a grizzly, you've already broken most of the rules in paying attention to your environment, and most likely, you are stupidly trying to defend a carcass from a hungry grizzly. Standing around firing a hand cannon, rather than seeking immediate cover, is a very quick and orderly path to becoming yet another statistic.
A .45ACP is simply not enough fire-power to kill a grizzly. Most .45s have muzzle velocities of 800 - 1100 fps and muzzle energies of 380-500 ft-lbs. You need something much larger and heavier with a muzzle velocities from 1200 - 2000 fps and muzzle energies from 1500-3100 ft-lbs. An ideal sidearm for Grizzly country would be a Ruger Super Red Hawk Alaskan snub nosed revolver chambered in .454 Casull Super Magnum or .480 Ruger.