If you're going to continue pursuing this then it looks like you're going to have to let her lead. I'd leave her with a "call/text me when you're free" and then get on with dating others while you wait for her to be ready to date.
I've found that when I met the man that I wanted to be with, I always had time to get to know him better.
What good is waiting for someone who has no time to date?
How long does one wait for someone that has no time to date?
Does someone who has no time to date ever actually bond with the person who waits for her to have time?
So many questions, so few answers!
One other thing: Is someone who doesn't have time to date sooooooo busy that they can't even return a text or answer an invite to do something when they are not soooooo busy? Don't forget her lack of manners while you're letting her do her thing, jlondinium.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion