Bob Bergquist, is an outfitter in Livingston and guides out of Geo. Anderson's fly shop there. I believe that Bob's wife operates a shuttle service called Hooter's Shuttle Service. The number I have for it is (406) 222-7979.
There are closer places to the Beartooth's than Billings and Livingston, but I presume you already knew that when you specifically mentioned those 2 places.