With a bear, any handgun is marginalized due to the low penetration when compared to a 5.56mm at close range.
A 16" barrel 5.56mm carbine with M193 ammo will drill through the thick steel bumper on a truck at close range. At that range, the hydrostatic shock will balloon the bear's head and the shockwave will shatter it's skull into fragments, turn the contents into mush, and the fragments will internally shred what's left. A close range, the 5.56mm out of an adequate barrel is a fearsome thing, even more so when you have 30 rounds on tap.
You can kill a bear will a surprising number of things, but you usually wind up doing the job with what you have on hand. For instance, one of the largest grizzly bears ever killed was dropped in it's tracks like a bag of wet cement by a desperation shot from a scared teenage Indian girl up in Canada with a single shot .22 and a single round of the now obsolete .22 long solid point.
For bear country, when you are not intentionally hunting bear, you have to have something WITH you when the attack happens. Since 99.999999999% of the time you are NOT being attacked by a bear, whatever you are packing needs to be small enough and convenient enough not to be a hassle or interfere with day to day life. Otherwise you'll eventually leave it at home when you should be carrying something 24/7/365.
With one shot remaining in his .44-caliber Magnum revolver,......
For a long time I packed around a stainless 5-1/2" Ruger Redhawk in .44mag and, as a minimum I always had a small two compartment nylon belt pouch with two extra speedloaders (the Redhawk and the S&W M29 use the same speedloader). Myself, if not carrying a big revolver with extra speedloaders, I'd opt for a Glock 32 with extra mags full of .357Sig.