Guests do not see your actual facebook page - just the profile picture. Take a look at your profile under Edit Profile (in the dropdown under your name on the top right of your screen) and then View Profile on the left to see what I mean. What they do see is your facebook profile picture, but you can change that. Still in Edit Profile, go to Photos, Symbol and Video. Upload your business picture - the same one you use on your facebook business page if you like, or something else. That will now be what AirBnB guests see.
Does that help?
Just a note that AirBnB does encourage hosts to use a photo of themselves, for good reason, I think. Photos of flowers, logos, etc., are less personal, and it is a trust platform. We do put ourselves a little more out there. Not that I don't understand your point. There are times my facebook photo would scare prospective guests away!