FWIW, all of southwestern MT is black bear country and of course the areas closest to Yellowstone are grizzly country. That said, in the 30-some overnights we've spent in the Big Hole, Rock Creek, Pioneer Mountains, and vicinity since 2010, we have seen no sign of black bears. I must here admit we did not necessarily keep the best of "bear country clean" campsites, either.
If I recall correctly, the Twin Lakes NF campground had bear boxes. I don't recall the various Rock Creek campgrounds having them. In WY, the FS 300 route through the Wind River Range passes by NF CGs at the Little Popo Agie River, Fiddlers Lake, and Louis Lake. All look like terrific places to camp and all are surely in black bear country.
Take routine precautions and you should be fine. It might be a good idea to include some phone calls to local ranger district offices to see if there are any warnings in effect for bear activity as you approach, though if there are, you'd likely see some signboard postings of such, so perhaps looking at CG and other signboards as you enter NF lands is a good enough check of local conditions.
Foy