I used to be ISTP many years ago - I was generally distant. A lot have changed since then though, so I'm finding it hard to relate to this lady. Either way, if I have someone I like, I'd try super hard to get closer to him. On the contrary, I'd try super hard to avoid someone I don't like, if I sense that the person may be trying to get closer, because I personally don't want to string someone along.

She just doesn't seem that interested but just going along with your flow - I assume it's because you're treating her for the meals. Maybe we just don't see her side of the story because, well, you're the one telling it... So you might as well ask her out directly, and move on if she rejects. If she gives unsure answers, then it's up to you to give her a time limit, but do yourself a favour too -- don't wait forever.