You're basically offering to be an AirBnB manager for them - take care of listing it, managing the calendar, dealing with bookings & turnovers, etc. So figure out what that deal would look like, and offer it to them. If there are short-term rental property managers in your area, see what they charge and offer something like that (although probably give better terms, since they're professionals and you're a part-timer). Otherwise come up with something fair. You might be able to negotiate somewhat better terms by offering them a floor on their earnings, because if bookings are bad enough you'll just move back in at the standard monthly rate.
But as a landlord, I would never do that deal. If I wanted to run an AirBnB I would do it myself or find a professional to do it for me. I would not do some bizarre half-breed deal with a manager that has (I'm guessing) zero experience and large time commitments to other things (training), and leaves me with most of the risks for damage to the property, pissing off the neighbors, fumbling tax/regulatory requirements, etc.
