The Minnow Bucket in Huntley is the nearest to TRR that I'm aware of. They always have minnows. Pryor Creek Bait shop in Laurel may have some leads too. The guy that runs Osprey Realty in Billings also has minnows, he is located behind the Billings Gunsmiths shop on Grand, check the phone book. If you are coming from the Eastern side, Red Rock Sports in Miles City usually has minnows.
As far as I know, that afore-mentioned guy in Hardin only has minnows in the summer. There used to be a guy in Ranchester WY and a pawn shop in Sheridan that sold minnows and were fairly convenient to TRR, but now the import of minnows from out of state (even though its the headwaters of Tongue River) isn't allowed.
My .02s.