No, you can't just "write off" the cost of rental property. Rental property is an asset which gets capitalized and depreciated over time. Typically, rental property is reported on SCH E as a physical part of your personal 1040 tax return, and the cost of the property is depreciated over 27.5 years.
If you have a single-member LLC, then absolutely nothing concerning the property will be reported on SCH C. It all gets reported on SCH E.
Now there are situations where rental property can be reported on SCH C. But one of the criteria for that is that you must provide substantial services on a recurring basis that are directly beneficial to the tenant. For example, daily maid service would be directly beneficial to the tenant. However, only providing maid services between tenants is not directly beneficial to the tenant "on a recurring basis".
From what I've seen, not very many short term rentals to include AirB&B properties, qualify as a SCH C business.
