To get a standard license (not REAL ID, not commercial class, just regular personal license) in WA you merely self-attest to your address. No paperwork/ proof required.

PO Boxes are generally known, if they don’t stand out by being address number, STE number, PMB number, etc or PO BOX number etc and if the licensing agent doesn’t catch it or doesn’t care, it is still fraud - the problem being if you get caught by the licensing fraud dept, whose job it is to catch it and care even more, then you need to extra prove your physical residence (and potentially have legal issues, but unsure if those get pursued).

Like others have said if the Air B and B doesn’t mind, use their address. The license comes in the mail in 2 weeks generally. And you can change address later (online, by phone or in office with WA licensing) once you’re more established. Best!