I've come across black bears in the wild, but thankfully never a grizzly. Personally, I'd just rather use bear spray because I'd hate to kill a bear.
Not to dish on that guy, but AFAIK most 'bear hunting' simply entails baiting the bear with some food, and waiting in a tree stand to kill it when it comes to eat. IMHO the bad ass hunters are turkey hunters. Turkeys are smart and really tough to stalk. You also have to often call them in, and worry about the wind, etc., which requires a lot of skill. I'm sure dropping a bear with a bow isn't too easy, however.
As an aside, I've eaten bear meat, and it is some of the most rank shit that I've ever put in my mouth. Just plain awful. Not even a flavorfull stew could mask its nastiness. I imagine people would taste better.