When it's dragged on with a lot of mixed signals and back-and-forth like this one where you've given chase and she's being coy, the best way out of it is to force a decision on her and then be done with it if she doesn't decide your way.
Her not answering a lot isn't a good sign... doesn't really matter how "busy" she is. If a woman's plowing 80 hours a week into school or work but she really likes you, she'll answer the phone (or call you back). Her apologizing over text ("Sorry about that!") is her taking care of your emotions; the quick explanation ("I was out having dinner!") without asking you what's going on, or why you called, or anything about you after you've tried calling her four times says she isn't lifting a finger to try to communicate with you or spend time with you.
I'd just send her a quick, "Katie, haven't been able to reach you, probably because you're demolishing your finals right now ;) Anyway, semester's almost over... let's grab a bite before we're out of here on break. Let me know when your schedule's open."
If she hems and haws, just tell her you can see she's really busy, and have a great break, very neutral. Then don't initiate contact again. She may start chasing you next semester, but you'll have to play coy and let her do all the pursuit and line up all the dates... all you'll do is give her the terms you'll see her on when she asks to hang out (e.g., only at your place, etc.). The instant you chase even once, even a single iota, she'll know it's back to the same as before and she starts running again and you start chasing.