Robb, (all)
I called the G&F in Jackson this morning. Sounds like they have quit calling hunters as per their regs and simply mail out a packet in July or August. The G&F gal said that they issued around 250 or so tags last year (bull & cow). Also, the bull tag this year is actually an "any bison" tag. She said that there were quite a few hunters last year that didn't fill their cow tag because the bison held up in Grand Teton N.P and didn't cross over to where they could be hunted. I assume that you have a bull tag.
The Nat. Forest is open all season (Sept-Jan 3), but you'll be put on a priority list for the Elk Refuge. The low draw numbers (us) would likely have the first opportunity for the refuge in late September, but you can ask for an alternate date. They are thinking about opening and closing the elk refuge on a week by week basis to let the bison wander in, so you might want to factor that in to your trip plans.
I'm inclined to wait for November myself. It can be pretty warm in Sept at times & I wonder about getting it out of the field quick enough. I do have horses though, so the warmer weather really shouldn't be that much of a problem. Be nice to wait until they're haired up too.
If I learn anything new, I'll post.
Don