Wyoming has a total of 24 tags, If I remember right 12 for residents and 12 for non-residents, but like mentioned only 2 hunters in the field at once.
Getting a tag will be like winning a lottery. Expensive, even for residents. I did some figuring and discovered I can hunt grizzlies in Alaska as a non-resident cheaper. My son still lives there so I wouldn't have to hire a guide. This might be on my plate if my shoulder ever recovers from having my rotator cup rebuilt. Even with a brake, my Model 70 375 still lets me know my shoulder isn't quite ready. Getting old isn't for the faint of heart.
In searching for brown/grizzly hunts, I discovered if one had to go the guide route, it would be cheaper to hunt these bears in Russia (Siberia) then Alaska or Canada.