Girl body language is really hard to figure out but when you do it will help.
After this long she knows you sit right behind her that is for sure.
She could be turning around for several reasons, like looking at something or someone else.
She could be turning around because she is glanceing at you or giving you the chance to show interest.
She could be turning around because she senses you are looking at her and is giving you the chance to respond.
Speaking from the female perspective, if she is looking at something else that is an opportunity to "show interest in her".
If she is turning around to glance at you,(again) this is an opportunity and she is (giving you the chance on purpose)
If she is turning around because she senses you are looking at her, (she is probably giving you the chance because she would ignore you if she didn't "want" a response.
You mentioned you are not making eye contact, but it is obvious that you don't know if she is looking at something else because you "quickly glance away" when she turns around. Make no mistake, she has probably seen you quickly glanceing away and knows you are looking at her. Even if she is looking at something else, she can see you out of the corner of her eye. Women do this, it is how they see who is in the room but shyly just like guys.
The easiest thing you can do next time is just get up the courage to look straight at her. She will see it out of the corner of her eye and she will either make eye contact or turn back around because she is shy also.
If she looks just smile. Maybe even say Hi.
Voila, the door is open. You can post again if your not sure what her response meant. But I bet you will.
