I spent a LOT of time in grizzly country in Montana. My girlfriend lived there (Whitefish) and we enjoyed hiking in Glacier, the Bob, Jewel Basin, Kootenai and the Yak.
What I found to be the very best option was some type of chest rig. I personally wore a small one made by Hill People Gear. It was just big enough to carry my G20, my wallet, cell phone and a small bag of quick clot. Its discrete and others don't even know your armed yet its very very fast to deploy your weapon if needed.
I'm right handed so I positioned the two zippers in the top right side of the rigs corner with a two inch or so opening so I could grab it with my left hand and "rip" the bag open and secure my pistol with my right. Very fast and works great.