You should be fine for gas. If things get desperate you can get gas at the Top of the World Store on the Beartooth.
It's fun to take some of the dirt side roads off the Beartooth and park and explore a bit. Red Lodge is a great town as well - good restaurants. It is a great overnight destination!
If you've never been to that part of the world prepare to be amazed. Even after going to the area for a few decades now I always find myself stopping to just take a moment to be in awe.