We will be spending Pesach in an Airbnb rental apartment. Must we do bedikas chametz on the apartment?
The primary obligation of bedikas chametz is at nightfall the evening (or, this year, nightfall of Thursday) before Pesach (O.C. 431:1, 444:1; Mishnah Berurah 431:1).
In a rental, the tenant is obligated if he has ready access to the premises. Thus, if the landlord gave the keys to the renter by the 13th of Nisan (this year, Thursday, 12th Nisan), the tenant is obligated in bedikas chametz. However, if the tenant does not take possession of the unit or did not receive the keys until late at night or the day of erev Pesach, the obligation to check the unit is on the landlord (O.C. 437:1; Mishnah Berurah 437:2-3).
Nonetheless, if the landlord did not check as required, you are required to do a bedikah when you arrive, to ensure that there is no chametz in the room (O.C. 435:1).
According to some poskim, the same is true regarding a hotel room. If you took the room before erev Pesach, you are obligated to do the bedikah at night. However, if you did not take the room until erev Pesach, the hotel is required to check (Shevet Halevi 10:68).