The fishing in the bighorns is fantastic. Some of the best lake fishing around. You can expect to find fish in most of the alpine lakes I think. By best fishing do you want the most/easiest fish to catch or the most challenging? As far as getting away from the outfitters up there, camp off trail 200' or more and travel off trail as much as possible. The outfitter camps are obvious, so you should be able to scoot right by them and find your own camp. Stay off pack trails if possible, these should be designated on the USGS Quads for the area.