Is she interested in me but shy or not interested and just being friendly?

[podrick]

First of all, I'm sorry for asking a question like this because I know how silly and common these questions are. However, I'm really confused and could use some help right now.
So there is this shy girl I really like and I'm pretty sure she likes me too, but sometimes I'm really unsure about her. We are pretty good friends, have almost the same route to school (so we almost always go together) and she has asked me several times to stay a bit longer in school for her and we always have a great time together and laugh a lot. There are a few signs that she likes me like laughing at my jokes, giving me compliments and once after school she just grabbed my arm out of nowhere and started running with me over the campus.
Other times, mostly when we are in groups or when others are around, she acts rather "cold". She still talks to me, but not as much as usual and she also won't really hold eye contact. She never really engages in conversation with me and sometimes looks right through or past me.
Also, while she does show some signs of interest, she never really touches me or stares at me (at least not in a way I would notice).
Now, I have already asked her to hang out some time, but she said that she was really busy with school stuff and that we would see. I know that she really was busy, as I had a lot of work to do as well. Still, she was rather surprised when I asked her out and didn't really propose hanging out another time.
A few days later she brought it up again and asked me if we could still do something together when school was over a few weeks later. That's when I became really confused, so two days later I texted her and asked her one more time, if she really wanted to, to which she replied "sure, let's do that some time :)". So I'm kind of sure she knows that I like her, eventhough I never really told her.
Now, I'm also kind of shy and might not show that clearly that I like her. I'm way too shy to just touch or hug her and also never really go up to her out of nowhere to start talking when she's with her friends. So maybe she acts this way because she's just as unsure as I am and wants to prevent me thinking that she likes me. But she's also one of the nicest persons I know, so maybe she only agreed to hang out with me out of kindness without really meaning (or actually doing) it.
So what should I do next? I'm scared that if I ask her again about hanging out, I appear as too clingy or even creepy and desperate. But I'm also scared that if I won't do anything now, she will keep thinking that I don't really like her. Again, I'm sorry for this question and every answer would be greatly appreciated!

[Dream_of_Waves]

It sounds like she sees you as a friend, not a love interest. This or she isn't interested in a relationship. I'd stop pushing it and just let it flow naturally. Some people are better as friends than romantic partners, and you would be surprised at how many nice women are out there.