Its alright if you're asking how to salvage the situation.
As said, it sounds like its too late, but obviously you're gonna want to play your cards anyway.
Disappear for a while and let her initiate contact with you. Its risky, because her tone sounds like she may actually not contact you. Wait a week or even 2 weeks if you're up for it, by that time a normal girl will probably have contacted you in one way or another. It doesnt matter how, it can be going out of her way to bump into you, or texting you something random.
After your mini break of a week or so, if she initiates contact, hit again with a date. Dont let her play hard to get and all that bs, go for a straight date. Assume complete interest, 'yo lets go XXXX'. To that, if she really is busy, wait for her to counteroffer or any suggestion for a future date. If she blows you off on that then **** it. If she doesnt text you for 2 weeks then go ahead and initiate again and try another date, if she blows you off or plays uninterested- then **** it. If you find another girl in the meanwhile- then **** it.
That's how i would play this. For future reference, when you ask her out, her response will be apologetic and will hint at when she is free or a counter offer of another date. Saying 'busy' with nothing else should be ringing nasty alarm bells in your head.