It sounds as if the reservation was not made at all if you did not accept her request in time for her to stay at your rental. In that case Airbnb will not pay you because you did not accept the guest timely. You will get a ding on your response rate and the guest will not be charged and there is no out of pocket cost to you. If the reservation was accepted and she backed out it, then she will be refunded by Airbnb based on your selected cancelation policy. Always refer guests to Airbnb when they request a refund. Never pay out of your pocket, all transactions should go through Airbnb.