Maybe the next time you are together and the moment seems "right" you could casually bring up some movie that looks good, and ask her if she would like to see it with you. If she says "no", just say "okay" and accept her response and talk about something else.
A movie may be a good first step, since there is little one-on-one conversing. After that, she may be able to move on to the next dating step.
Just a thought.
Good luck. I am keeping an eye on you. You are giving me hope.