I've been living, working, and hunting in Montana grizzly country since 1975. My first 3 years we lived at a Forest Service Ranger Station between Whitefish and Eureka, MT. I killed an elk and a deer there each of those years. My only centerfire rifle then was a .30-06. I wasn't allowed to carry a firearm at work, but recreating there I usually carried 1911 .45 acp or a Ruger SBH .44 mag.
My whole time there, working in the woods about 8 months of each year, deer, elk, and bird hunting and berry picking, I only saw 1 grizzly bear. I saw it one spring while driving on a FS road. It was eating some vegetation beside a small creek about 50 yds below the road. I watched it from inside my truck for about 5 minutes. Then I got out and sat on the side of the road to watch it. Almost immediately his nose went up in the air as he smelled me, and he ran up the slope on the other side of the creek and dissappeared.
In 1978 I moved to where I still live about 6 miles SE of Bozeman, MT. In 30 years of working in the woods for the Forest Service here along with another 18 years of hunting, fishing, and recreating in the woods here, I have only encountered 2 grizzly bears.
The first one had found a dead horse near a FS trail south of Big Timber, MT and just north of Yellowstone NP. The FS District Ranger had gotten reports of this bear charging horseback riders on the trail there, so the Ranger called me to "dispose" of the horse carcass. One of the District employees went in with me to dynamite the horse carcass. The bear was on the carcass when we got there, and it ran off into the woods.
After we blew up the dead horse, there was nothing left of it larger than a Mac D hamburger that the bear, coyotes and birds would clean up in a few days.
My 2nd grizzly encounter was in the mid '80s when two of my friends and I were hunted in the mountains just north of West Yellowstone, MT. We had my two horses and we were camped at the end of a FS road. We had the quarters of two bull elk and a bull moose hanging in the stock rack in the back of my truck. Just before going to bed one night I went out to check my horses, and a grizzly bear was on top of the road cutbank above our tent. He woofed and clicked his teeth at me.
I had my Ruger SBH .44 mag with me, and I fired one shot just over his head. He didn't even blink, so I fired another shot into the trunk of the tree next to him. Again, no reaction from the bear. So I holstered my .44 and picked up a rock that I threw and hit him, and he ran off.
There was another camp that also had an elk hanging about 1/4 mile down the road from ours. A few minutes after the bear left our camp we heard 5 or 6 quick pistol shots from the direction of that camp, and a half hour later we saw their headlights of them leaving.
The next morning I saddled one of my horses and followed the grizzly's tracks in the snow. He had gone from our camp directly to the other camp, then after their shots he ran to the far end of the timber clear cut where they were camped, then turned and came back near our camp.
When we left we reported the incident to the MT FWP. The bear had a radio collar and ear tag, and had been a problem bear near Cooke City and had been trapped and released near where we had been camped.
I later learned that he had hibernated a few miles of where we saw him and the next spring they found his collar near where he had hibernated.
Not an encounter, but a few years ago a bow hunter hunting in the field across from my house had filmed a grizzly bear. The next day, my neighbor found grizzly tracks in the snow about 350 yards above our houses.
I respect bears, but I'm not paranoid about them. Keep a clean camp and hang your meat away from your camp. Just about any centerfire hunting rifle has at least twice the energy of even the hottest magnum pistol. Keep your pistol, rifle, or bear spray with you and know how to use them.