Hmm, sounds tricky.
I would say that you shouldn't give too much of yourself too fast, i.e. committing yourself by way of (say) a relationship or (perhaps worse) a one-night stand before you've worked out what she's about. Carry on trundling along with it. You can take things slowly as it were, and end it if you don't like her intentions before you get too deeply embroiled. Worst that can happen if you only take things slowly is that you get made a fool of.
Plus, it could well only be that she's been too nervous about talking to you nicely before if she wasn't sure what you thought of her, hence the 'treat him mean, keep him keen' act. I personally don't understand those kinds of mind games, but it might be what she's doing.