The Art Association of Jackson Hole has a darkroom. I think they used to rent it but not sure about that now, and I think it would be very expensive. I don't know where you could get a single-use camera with Tri-X in it.
There used to be a place called "The Darkroom", on Gregory Lane, but I don't think it is a going concern now. They used to rent their darkroom and had classes. All I have is their business card from who knows when, and I never went there. I use my own darkroom.
Is it that hard to travel with film these days? Are you concerned about X-rays at the airport?
If it was me, I would just take a good camera with film, and ask for a hand-check. Lots of photographers come through here so the TSA people are used to it. Most people use digital cameras, of course.
I live about 25 miles from Jackson. I fly out of their occasionally, and have never had a problem with film being fogged (100 or 50 ISO though, and two years ago or earlier).