My friend who hunts in that area carries a holstered 10mm handgun, in case his rifle is slung on his back.
There's a great picture out there/here with a gal fishing with a 44 in a chest holster. That's what I would want if I were in Grizzly country.
I live in between Big Sky and West Yellowstone, MT, in prime bear territory, on a number of acres. I usually carry a 10mm or a 45-70 when I am working on the property. Just last week, I came across a grizzly in the woods and wasn’t carrying. He was about 30 yards ahead of me, I stopped, and he decided to keep walking the direction he was going (left to right, in front of me). I was very fortunate and highly disappointed in myself for not being protected/prepared. In 25+ years, it was my closest call on this property.