Girl tells me to call her anytime, but now she avoids me... sort of. Help!

DrJones
I've read lots of very similar stories from other guys, so here's mine:

I'm attracted to someone who I've known for a while, but we've never been close. Recently we hung out a few times - just the two of us - and it was fun. We got to know each other some, though nothing physical happened.

She acted interested in me and told me I'm awesome, we should see each other more often, and I should call her any time. So, I invited her out for a few more casual date-type things (get a drink at nearby bar, eat ice cream in the park, etc.) Each time, she said "I have to [insert other plans here] but that sounds fantastic." I'd say something like "OK, maybe later," and then she wouldn't respond.

Then I ran into her by accident at a bar and again at a concert. Both times, I went to talk to her and her friends, she spent a lot of time on her phone and hardly said anything to me, I backed off and went back to where my friends were, and she left without saying goodbye. (I could tell she had been telling her friends about me, though, because they knew a lot about me.) Then the other day she sent me a text out of the blue telling me she heard my band online and thinks we're pretty good. I sent her a thank-you text, and that's the last we've heard from each other.

I'm pretty sure she's into me and is not "playing" me, she's just not sure what to do with me. I suspect she just started seeing someone else and doesn't want to tell me, but I don't really know that. Maybe she wants to be friends, but nothing more than that? Or she's just nervous because she has strong feelings for me and that scares her? I know she can be a very moody person, so maybe this is just how she behaves? (She's a college senior, to answer any age/experience questions.)

I'm OK with any of these possibilities, but the suspense is making me slightly crazy. If she's dating someone or just not that into me, I'll be disappointed but I'll get over it. If it's nerves or moodiness, I can accept that and deal with it.

I'd like to show her clearly that I'm interested, but in a way that's not needy or demanding. Or, is it better to just leave her alone and move on? Ladies and gentlemen... what should I do?
Updates
+1 y
Basically gave up on her and didn't call/email/text/etc for a week or so. Yesterday she texted me back asking, "When are we going out to [bar I had suggested earlier]?" I told her I'd have time for that tomorrow and she never replied. Huh?
Girl tells me to call her anytime, but now she avoids me... sort of. Help!
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