The regulations are diverse not just among jurisdictions but even individual ranger districts within a single national forest! Plus some states and counties have their own thing (such as California's requiring a state fire permit even if you only use a backpacking stove).

The rules will also depend heavily on the fire danger at the time you go. So call the Bighorn National Forest maybe a week before you leave, which will give you time to pick up a different stove and fuel if necesssary. Try to speak to a wilderness ranger rather than the clerk who answers the phone, if you can.

That's an area I always wanted to visit, but somehow I never get farther east (from Oregon) than the Wind Rivers!