What Nyseto said is far much better than "calling her BS". That is a sure way to not get anywhere. Just imagine that someone tells you that, you will become defensive and will want to avoid that person.
About what happened: In his Anihiliation Method, Style says that is always your fault, you weren't good enough, your game was lacking. It is funny that I have applied that to everything in my life but to social skills. Something went wrong at work, it was my fault and I will improve for the next time. Someone was beating me at sports, it wasn't because he will be always better than me, or that game wasn't suited for me, I knew that I needed to improve and become better (and the fact is that I did). Now that finally I have been show that I have to apply that same mentality to social skills, I have started to improve (finally

).
Two points from what you have described:
- You ask her once if she feels awkward and wants to leave, you're thinking on her well being. You ask her more than once, and she will start thinking that you
want her to leave. Maybe that night she will still let it slip, but in the morning, once she is thinking about it, she will get that impression.
- The same way that you cannot invite for dinner, or coffee, or anything in which the objective is to be you two alone, you cannot accept quickly that kind of invitations. Say that you have a previous commitment or similar, and then offer about doing something else that you were going to do ("I am going to shop for a hat ...")