You might try the visitor center at the southern entrance to Yellowstone. We drove through Yellowstone on our way to Nomad View and I remember stopping there. They definitely had gas and I recall dumping there also. Maybe a phone call or Internet search.
Also if you are going to Nomad View, I suggest going to Upper Nomad View (up the dirt road further). Views of the Grand Tetons are spectacular.
41' Forest River Cedar Creek2014 Chevrolet Silverado 3500HD LTZ
Answered on 5/21/2020:
We went to Frontier Cabins, travel North on 240 (towards Wall, SD). It was a few miles from Nomad View Dispersed. On the side of the check in building is a water spigot. We asked if we could fill our water bladder and they said it wasn’t a problem at all. Always talk to them first but they were very nice about it.