Make sure you are in one of the areas that Air BnB pays the county assessment for on your behalf.
They will collect them if you list them as one of your "taxes" /fees to collect- but they include them in the amount they remit back to you and in its your responsibility to file the monthly report and pay them to the correct organization. In some areas they have established counties that they do collect them and remit them on your behalf - but that is not the case in all areas. You can call the county and ask them. They will know. You will see them listed in your pay out under the name of what ever you put them under.
In my area, they collect them, but do not submit them so I file the report monthly and they with the state quarterly -which is what I am required from the state to do. STRS are responsible for getting the required license/registration from the city/county and paying the fees. It has just really been getting enforced in more areas in the last year or two.
I attached one of my suite payouts so you could see what I was referring to. When you look at your remittance statement they are listed under property use tax. You actually don't collect sales tax from customers- you collect Use tax. Rooms/houses are items they use - not purchase - so its a Use tax you collect though most people refer to it as a sales tax. My county assessment is 5% and my state use tax is 6% so they collect 11 % on the room rent. In most counties you do not pay the county assessment (5%) on any other fees -so the cleaning fee is only charged the 6% state use tax. Its a tad confusing at first, but once you get used to it - it goes it takes a few minutes a month to deal with. Hope that helps! 
