I would say during rifle season, your best bet for a nice buck would be dropping down into a canyon where they is a clearing along a water source, and then sit there all week long. It is a low percentage game, but if you are patient you will eventually catch a decent buck coming to the water.
Chasing them around in the timber is more than likely going to be an exercise in frustration, that being said sitting by a water source might be too.
What you will find when you get there is that after you drop of the ridge you are in black timber, and spotting from any distance is difficult at best. You might have some success glassing the lower edges of a burn (hint: lots of the bighorns burned last year). these always tend to be game rich areas.
I would recommend ordering a forest service map and getting the "GPShuntmaps" files for google earth and going from there. My two nicest muleys came out of the northeastern corner of the Bighorns (they are both in my photo gallery if you want to see what I have been able to drag out of that area).