I agree, she might have been anxious and so she was just off her game. One of the most awesome people I know was 100% like this our first meeting. It turns out, talking about herself was how she dealt with anxiety at hanging out.

I recommend inviting her to a couple group events, and see how things go. It'll let her hang out and have a chance to make more mom-friends, and it might also (especially as she goes to a couple of them) give her a chance to become less anxious. If you invite her to another one-on-one, though, it might send a message that you're developing a close bond. So I'd stick to group stuff until you see what she's actually like.