I've been following this thread closely since I had the fortune to have drawn a nonresident bull tag last year. I have some info that hopefully can help this years and future years tag holders.
First off......congratulations on drawing an awesome tag! I was only on the priority list for 3 years but know guys that have been applying for 10+ years with no success.
Since I knew as much about bison hunting as I do about hunting elephants (about none!) I decided it would be well worth my time to hire a professional to help me out. I chose Rick and Kelly Miller of Double Diamond Tag and Drag for our hunt. Trefren Outfitters is also licensed to guide on the Refuge.
Upon ariving in Jackson and checking in at the Game and Fish office, the first item my wife and I learned about was the relatively small amount of land that is open to persue the buffs compared to the huge amount of National Forest land surrounding the Jackson area. We went hunting in mid December and by then even more public ground is closed to give the elk herd winter refuge. Since this is the case, the Elk Refuge and the remaining open forest land gets hammered pretty heavy. Road hunters were everywhere. If you can bring horses to get away from the roads,so much the better. The outfitter's phones were constantly ringing with hunters checking in to see if the herds had moved to the Refuge yet. Also, if hunting the National Forest, be extra sure that you are in the forest and not in Grand Teton National Park. The boundry is marked all the way from Moran Junction to Jackson but the markers can be a little hard to find sometimes.
The Elk Refuge hunt can be an awesome experience or a very frustrating one. After the opening day shootout, the herds will move off of the Refuge and (especially the cows )probably will not come back until winter weather forces them to. Bulls may filter through at any time. During 6 days of hunting, we hunted the Refuge on the first and last days and the National Forest on the remaining 4 days. There wasn't enough snow on the ground to move the herds to the Refuge as they normally would have done.
The final day we hunted, there were 10-15 hunters on the Refuge with us. Except for the northern end of the Refuge, there isn't alot of stalking cover. For the most part, the Refuge is one large valley with little topography. Everyone was courteous that final day, but all wanted to fill their tags. I called it "organized chaos"! The buffs were out in the open and were pushed around by different groups of hunters until they ran out of steam and stopped to rest. We followed them on horseback but most hunters were on foot. Seven animals were taken that day but the Game and Fish officials told us that during the prior year, almost 50 buffs were shot in one day! They said that bullets were flying everywhere that day!
As Wymoosehunter posted earlier, it is well worth the money to hire one of the tag and drag services once you harvest an animal. If more than one animal is down near yours, they will probably make you one hell of a deal to get your business as well as the other hunters. We had 4 animals down in the same area and 3 out of the 4 buffs were drug out. The other guy wanted to handle his own cow. He was still working on getting his buddies to help him out while the other 3 animals were already loaded and on their way out of the Refuge. The tag and drag guys also gutted the bison and took all of the required samples that the Game and Fish requests.
A couple last bits of info. If you can, make sure to bring along a limited range weapon (shotgun, muzzleloader, bow, or handgun). The southern end of the Refuge now has an archery only and short range only area. When pressured, the herds tend to retreat into those areas. Also, make sure that you bring the largest rifle that you can comfortably shoot. I used my .338 Win Mag and wasn't over gunned. They can be very tough to bring down, Their heart is as big as a man's head!
After our experience at Jackson, bison have become one of my favorite big game animals. The meat is just awesome! We're having a 1/2 life mount of our bull and having the skull bleached as well. Please feel free to P.M me and I'll try to answer any other questions that I can.