first come first basis is fine
but, why you ask her to pay you first before viewing the room?
she can just view it first, and pay u on the spot if she wants to book it. but no way to just pay u first before viewing the room.

if she viewed the room and said will pay you later, and keep delaying the payment for like 3 or 4 days, no harm for you to find other tenants as she broke her promise.

and since she is not free to view the room and you got other potential tenants, just rent it out and tell her that the room is no longer available. she won't lost anything and you didn't lose anything as well.

but asking ppl to pay before viewing is wrong. you think this is cinema?