Lately the Grizzlies have not been confined to "The Back Country" in Montana as they once were. They are spreading out and being seen in places that had no Grizzlies. Central and South Central Montana come to mind, well east of the Rockies.
I have read of, or known, very experienced Montana and Wyoming hunters, natives all, that have had their dance tickets punched by Grizzlies, even when they did everything "right". None died, but man were they torn up.
I have found myself in "close encounter" situations a few times, and it gets your senses on full klaxon. A sow with cubs or any bear on an animal carcass is something you want to avoid at all times. Be very aware of your surroundings and stay as much to open country as you can. Bears have a disturbing body odor. If you smell something foul and out of place, get away from that area. If you see evidence of "rooting" (looks like an excavator was tearing up the ground), get away from there.
I'm not telling you not to go and enjoy yourself, just be savvy about the country. Talk to Forest Service folks, game wardens or locals before you go on a hike. I'm a Montana native, and I carry a Glock 20 when I'm about in the back country. I haven't had to use it, and that's the way I want it to stay. As for me, if I have to use it to defend myself, I've stepped in it big time. It doesn't hurt to carry bear spray as well.