Steve, Joe is right - be sure to check with the local fly shop. But in most of the lakes in the Beartooths (and streams too) the fish aren't especially finicky. Take your standard dries and streamers; attractors and terrestrials(adams, wulff, grasshoppers, beetles, PMD, baetis, wooly buggers, etc) and you'll do just fine.
The better fishing in the Beartooths is lake fishing so you might consider a spinning rig instead of a fly rod. I don't have one but wish I did every time I camp by a lake.