Are you coming from the Jackson hole airport? Uber or Lyft are now available there I've heard which eould orobably be your cheapest option. If don't have access to them, you could get just get a cab or the airport shuttle. If you end up having to do that, it would make sense to just take thr cab/shuttle to the town of Jackson and taking the START bus from there (extremely reasonable fares).
Uber, Lyft, and the cabs at the airport are all about the same ($50-$60 one way). If you book a shuttle through something like jhshuttle ahead of time it'll be ~$30 one way.
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