@jespah,
Thanks a lot, @contrex, @jespah, @PUNKEY.
@contrex - I don't think the reason is shyness. We used to regularly meet in person earlier (as the original post states), and she simply isn't the shy type. In person, she's quite assertive and outspoken, and it's hard to see why she'd be shy when messaging. Also, the point is not that I'm not interested in her (I am), but it is that, despite being interested in her, it feels awkward to message someone who never starts a conversation herself.
@jespah - I think you're absolutely right. I've was thinking along the same lines myself, and I think your 'I'm bored, why aren't you entertaining me' description absolutely hits the nail on the head. Thanks a lot.
@PUNKEY - We both agree with @jespah that she's just fishing for attention, so now the question is: is there anything I can do about this? I'm not turned off by 'too much work', as you think. The point is - what 'work' can I do to pursue a girl who apparently thinks of me as free occasional entertainment? When she sends me a 'panic' message, I reply immediately, and we talk for a while. That obviously doesn't change anything. I've been planning to do what you suggest - cold shoulder her by saying 'been busy' - when she eventually texts me. But I've never gotten around to doing it. I guess I'm scared that, if I do that, she'll just find some other form of free entertainment, and stop messaging me completely. And since I'm interested in her, I'm sort of dreading that, even though I know that I'm just disposable entertainment to her.
The question is - is there anything else I can do to swing things in my favor?