I agree with 22-rimfire that if you are hunting with a long gun, there is no benefit to adding a handgun on top of that.
For general woodsiness where you are worried that you would be attacked by bear, I'd say you want a revolver, in .41 or .44 Magnum, ideally with a 6" barrel. Not only are these more powerful than the 10mm, but there are readily available loads appropriate for bear for these magnum revolvers.
The odds are that you'll never have to defend yourself against a bear, but, if lightning strikes and you actually need to, I'd want to use something that has a real good chance of working. IMO that's at least a .41 Magnum with big game loads. For grizzly, .44 Magnum is more appropriate.
Handguns designed for antipersonnel use aren't going to be reliable on bear. Bear are thicker and have bigger bones than people. Your choice of firearm and load has to take that into account.