Shes obviously into you. The fact that she has a BF shouldnt bother you. She has the right to choose whatever she wants.
Just dont press her into making a choice. As long as she knows that you understand her situation thats fine. So, she has a BF, who cares? That kind of things happen all the time!
You might wanna keep the whole dating thing out of it. Asking her out or asking her to the movies is too much of an eye opener. She will see what she is about to do and that will clear her mind and fuck up your game. She will get ... aaaah... I cant even say the word, bad feelings and regrets...
Better to just let it happen, do friend stuff, just let it happen so that you happen to be alone some time. Have a great time and go with the flow, its flowing in the right direction as it is.
She can claim that she didnt know what she was doing and that it "just happened". That is the best excuse a girl knows. Let her have that. It just happened.