In brown bear territory the minimum you should be considering is a 44 Mag with heavy deep penetrating cast or punch bullets. In a brown bear encounter even a heavy loaded .357 will lead to you ending up as bear scat.
For a protection gun, I would try to stick with a double action revolver such as a SW model 29, 629 or a Ruger Redhawk or Super Redhawk.
A packable gun that you can keep on your person (not much good in your pack) will probably end up with a relatively short barrel 4" or less and will have substantial recoil if fired with full house deep penetrating loads such as the
Grizzly 300gr WFNGC.
Not being a terribly experienced handgun shooter you should be wary of going to calibers higher than the 44 Mag (not necessarily avoid, just be very judicious in your decision). While packing a ton more punch the 454 Casull also packs a ton more recoil, especially in a packable platform such as the
Ruger Super Redhawk Alaskan. Unless you are VERY familiar with shooting guns that dish out this type of recoil they can be extremely difficult to shoot (the followup shots tend to take much longer). Take a look at this
youtube video
Another good review of the 454 Alaskan is from Shooting Times (
here)