How to handle situations like this?

Let's say you asked a girl out on a date a couple times and she turned you down both times. The first time she turns you down, she gives you an alternative of maybe next week. Next week comes, you ask her to join you for a drink again. She's gives you another excuse on why she can't.

You next her and continue on with your life. She contacts you out of the blue a few weeks later. How should a man handle this? Do you take her reaching out to you first as an opportunity to ask her out again? Even though she turned you down twice. Or do you wait until she asks you out on a date, in which you can make her wait awhile before you become available.