I live in Bozeman and most of my regional hiking is in the Greater Yellowstone Ecosystem, much of it solo.
Hiking in grizzly country is just like hiking in black bear country.
Until you actually see one. Then you wake up.
You really wake up when you have an up close encounter, and by the time you experience a charge, you pretty much realize that humility and recognition that you are not in control takes a front seat to any preconceived notion of security.
Hiking is not so bad, per se.
Hiking at night, on the other hand, is just plain scary. That doesn't mean I don't do it, but I'd be a fool to pretend that I didn't have some terrifying night hikes in the Yellowstone area as a result of spooking a bear off the trail or hearing large animals crashing through nearby brush.
Then there is the whole camping thing. Normally it's not so bad, unless you know from fresh sign that there is a grizzly in the area, then you sleep...not so sound.
It's extremely cool. Knowing that such a magnificent animal is part of the ecosystem you're enjoying, and knowing that you aren't top dog in that ecosystem, it's just a neat, humbling, deeply satisfying experience.
Whether it's a good idea or not depends on your perspective and values and what you want out of wilderness.
For my wife, it's not a good idea. She doesn't hike in griz territory. She doesn't like it, and she doesn't enjoy the stress.
For me, being solo in the proximity of a grizzly bear is incredibly rewarding. I love it.
To minimize your probability of an encounter, you can select your hiking destinations accordingly. There are lots of bears in Yellowstone National Park, and in the western half of the Absaroka-Beartooth Wilderness, and the Teton Wilderness. There are fewer bears in the eastern AB Wilderness and the Washakie Wilderness, but they are there. There are very few in the neighboring Wind Rivers, Tetons, Spanish Peaks, etc. So, bottom line: lots of places to hike where you can avoid them if you like.