While it's very outside the standard Airbnb experience, you could try it.
You would have to make very clear what you are offering.
Your Headline should be something like
"Bedroom suite with Toilet, Sink, No shower or Bath"
Your first message to your guests should go Like this
"Thanks for your interest. There is No shower or bath. Would this be OK?"
If you price your product low enough, you could get business. Not everyone is into bathing everyday. However, because you are so outside the standard you will need to be very careful who you attract. Druggies would be very attracted to your offering. And attracting guests to do business at your place is a different world. Porn shoots? Selling guns?