I will pass on every bit of advice that all the people I personally know in Grizz country, along with my own experiences in grizz country. Most of my friends/close acquaintances that live and hunt in Montana, Alaska, and Idaho all carry a caliber that begin with "4" or "5"; 41 Mag, 44 mag, 45 Colt, 454 Cassull, 445 Ultra, 460 S&W, and 500 S&W. I personally carried a Blackhawk in 41 Mag with 215 grain slugs in a chest rig. I have been hearing rumblings from my compadres in Grizz country more than half of them are transitioning to Glock 20's (10MM) because they have more rounds and lighter top pack. the 10MM is comparable to a 41 mag in a semi-auto. I can not shoot the Glock platform so I would build a 45 Super or 460 Rowland in a Para-Ordnance, or a wide body Caspian with a 6" barrel. I will get the same amount of shots with a 200 or 230 grain 0.451" diameter slug.
I have been told that 180 grain hard cast and jacketed soft point slugs in the 357 Mag will keep a bear from getting any closer if you can put at least 4 shots in his face. but I can not confirm this. I have only hit 2 Gizzlies ever. those were with a 45-70 and a 338 win mag. I never had to use my side arm. I smelled the bear before he got too close.
My best advice is shoot what ever you are most familiar with, use proficiently, are accurate with, and practice with it until you are nearly as good with it as you are with your rifle. ALSO carry a long shot bear spray. in very close quarters it disorients the bear (can't smell and see) and you can either get out quick or the bear will turn around and "pinball" away.