Why is she doing this? It's starting to annoy me

Just back off for a while and see how she reacts... if she doesn't care, then she doesn't like you, if she tries contacting you then that means she misses you and possibly likes you.

Shes just playing games to see how long you stick around

Sounds like this is being hot and cold. Her actions are very inconsistent. If I were you, I would not allow her to tag along with me anymore until she got her act straight. I would also act has If I am busy when she invites you to events has well. Why should you make yourself available to someone who won't do the same for you? She will notice this change in you and ask why. You should then cease the opportunity to tell her how you really feel.
Don't stay hung up on her and try to find a woman that is out there, that has time for you (and doesn't play games)

Honestly man if a guy did that to me id try and confront him about it because you don't deserve your head to be screwed with like that, if she continues this then just walk away because you will never really get anywhere with it, I always constantly get my head screwed with by guys so I know how it feels when you don't know if your coming or going, you gotta be tough with people these days as a lot think they can just walk all over people, it's not fair or funny at all. I was just dating a guy for almost 4 months and I ended it when he told me he could be taken from the country any time and I wasn't sure how I feel, I just feel like there is really no spark there at all but yeh... he says now he only really thinks of me as a friend so pretty much those times I spent kissing him he was just having fun :\ yeh... not amused lol, so don't let her screw you around.

i can see why this is annoying.

It's hard to say why she's doing it. She may like to play games, she may be playing hard to get, she may like you pursuing her and the control it gives her in the relationship

whatever the reason you need to address it with her. Tell her how you're feeling specific events that are leading you to feel this way. Tell her you want to hang with her but aren't into all the flaky wishy washy behavior

She knows you like her and may be taking advantage of you as a result to do things she wants to do when she wants to them on her terms you need to make sure she isn't doing this because it can quickly lead to (and seems like it is already) her showing you and possibly feeling a lack of respect