I just finished reading "Handguns for Bear Protection" in an old issue of Handloader.
It was noted that Phil Shoemaker, a noted Alaska guide, carries a 4" .44 Mag S&W. His daughter carries a S&W .357 Mag.
Both stoked with heavy hard-cast SWC bullets.
It was pointed out that a mad bear can cover ground at about 30 MPH, and the time from warning to full attack will run about 2 seconds.
SO, you will be in a fight for life with a bear, while on the ground, with it on top of you, before most folks can unholster a gun and get off a shot.
At that point, all that can save you is deep penetration that can break the neck or penetrate the throat and lower jaw and hit the brain or spine.
That dear friends, is no place for a 4 1/2 pound .500 S&W that is liable to knock you unconscious when the recoiling gun hits you in the head at the first shot.
The author, Brian Pierce mentioned the overwhelming popularity of the Model 29 Mountain Gun for it's fairly light weight and controllable power.
More recently, he mentioned a bear hunt with Shoemaker in the last year or so, and both he and Shoemaker were carrying 329PD's.
It has also been noted that finding a Mountain Gun or 329PD in Alaska is almost impossible, because the locals buy them faster then the dealers can get them.