In an area with a lot of black bears, it would be a good idea to carry a .44 or larger sidearm for self defence (works on two-legged predators too BTW).
In an area with lots of grizzlies though? Well, I’d recommend a 12 ga. with slugs or something along the lines of a 45-70 Guide Gun.
The .44 is a fine pistol cartridge... but it’s still just a pistol cartridge. To give you an idea of the world of difference between a pistol and a rifle or shotgun cartridge, check out this fun page: http://www.theboxotruth.com/docs/bot5.htm
This is what a padlock looks when it’s hit by a .44 Magnum: http://www.theboxotruth.com/images/5-5.jpg
This is what a padlock looks like when it’s hit by a shotgun slug: http://www.theboxotruth.com/images/5-14.jpg
The Forest Service used to issue .375 H&H Magnums to their folks in Alaska...sounds about right to me.
Of course, that was 30 years ago. Now, they probably issue talking points and tapes of classical music to play while you are being mauled.