Simple: ask her to mail a check as holding deposit. Once you have the check you will stop showing and wait for her.
Difficult: you dare not to ask her, she might not mail the check, but you really really want to rent to her.
This is like dating, either you think there is plenty fish in the sea, or you think she's so special you just have to have her and not consider others.
Be a shark, not a minion.