My date is trying to keep me on a leash

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So I've started dating this girl a while ago. We went on a couple of dates but nothing really happened. She seemed really interested every time but sort of "kept her distance" if you know what i mean(I could put my arm around her neck, but she wouldn't allow me to hold her hand). So I asked her on a third date and she told me that she is busy and can't go in the next month

I took that as a nice "Sorry but I just don't like you", swallowed the bitter taste in my mouth and moved on. But since than she continued to flirt with me and text me every 2-3 days. We continued to flirt so I thought it would be logical to revoke that third date again. Of course she refused it again, saying nicely she is busy with collage and other bullshit. But she still continued texting me. Sometimes even daily


This has been going for a month now. I've been probing her and testing to see how she would react to some things
>she texts me two days in a row first
>I text her first the next day
>she responds vaguely like she is interested
>she doesn't text me for 4-5 days and than she continues as usual

The weirdest thing is sometimes she starts a conversation for absolutely now reason
>Hey anon, what are you doing
And than just plays uninterested for the rest of the conversation answering with short text and vague answers

Now I am not going to call her on a date again obviously, I fell in that trap 2 times already. But I don't know what to do or how to get out of this shit. I would be more happy knowing she doesn't like me than this bullshit where she gives me some hope every couple of days or so

So my question is: Is there a way out of this or should I just let it go until she stops texting me completely ? So far I played "hard to get" too and whenever she would text me I would try to mirror her
>act uninterested and bored