You can argue--and many do--that pepper spray is a more effective bear stopper than any gun. We'll leave that aside for now, because this blog is not called "The Spray Nut." Instead, we'll assume you have already debated guns vs. pepper spray and opted for a gun. (Or you may decide to carry both.)
Not surprisingly, I would tell you to take a shotgun over a handgun. Shotgun slugs have about three times the muzzle energy of a .44 magnum and make much bigger holes. Unless you are a practiced handgunner, a .44 magnum is a difficult gun to shoot straight--even at a very big target.
The gun should be a reliable 12 gauge pump with a 18 ½ to 20 inch barrel and should be smoothbored with an Improved Cylinder choke.
The barrel should be plain with nothing more than a brass bead, if that. Iron sights won't be necessary up close and might catch on something at just the wrong time. I would fit it with some kind of tactical sling that would be comfortable for carrying the gun through the brush for days on end until I finally, urgently needed it. And, while the standard magazine-full of four shells should be enough, a magazine extension might make you feel better.Whatever gun you choose, it should have a safety located in the same place your other shotguns have safeties (top, front of trigger guard, back of trigger guard) so you can take it off without thinking.
For ammunition, a fullbore slug like a Foster-style or a Brenneke is the best choice. Sabot accuracy doesn't matter, because you will only be shooting at a bear at range of a few steps.