For a less expensive (especially on senior pass) site, but with electric only, check out the Baker's Hole NFS campground a couple of miles north of West Yellowstone. Electric only at about half the sites, no dump station, no water hookups. We paid $6 to dump tanks at Grizzly on the way home.
There are some very nice, large, private sites at Baker's Hole---it is a campground, as opposed to RV park. Get there mid-week for an electric site, unless things have changed, there are no reservations.
Grizzly is a very nice RV park. By far the best option in the area if you want hookups.
Single empty-nester in Middle TN, sometimes with a friend or grandchild on board