You Will see bears if you spend any amount of time there.I have a cow tag this year in 54. Northwest of Cody. Pretty good Grizzly population up there?
I hunted the area in 2018 with 4 guys. We encountered a total of 6 different bears in 7 days of hunting and 1 bluff charge. Any where around Cody in and around timber you are going to have bears around. The 6 bear encounters were VERY spread out in that area and not concentrated to a specific trail head or area.
Even so, I am moving there with my family in the next few months. The bears need to be respected and proper precautions taken. Some great advice in this thread, but they shouldn't keep you from recreating in the area.