Have to agree on Fishing Bridge, it is A SARDINE campground! There are some electric hookups on the East Entrance Road of the Shoshone Forest, electric only, but only 15.00 for Seniors, not sure regular price. Wapiti and Rex Hale have electric. Lots of dry camping on that corridor too.
West Yellowstone has lots of RV parks and some Forest Service with electric only, You can dump at Grizzly RV campground for 7 dollars.
Just a thought, and ideas....