Information:
Both of us are college sophmores
In a fraternity
I get the feeling that she is the religious type
Met her last year and was friendly with her, asked her to formal and found out she had a boyfriend

This year, in one class with her. I asked her if she wanted to do homework and study with me one day, she said yes. That night I checked out her Facebook and found out she is now single. I'm guessing less than a month but not sure.
When we were studying, it was mostly buisness, I was asking her questions every once and a while not relating to work and she gave her answers but didnt open up much to me. Tried to do an opinion opener with her, same result.

Asked if she wanted to meet up again to study for a test we have. We are meeting on sunday.

What is the best way to go about this and subtly show her i am interested in her and try and win her interest.

I cook for my mates alot, was thinking of asking if she wanted to come up to try it sometime but we are in completly different circles of friends so I doubt she would be comfortable to me randomly asking to cook her dinner and my mates being there.

Any input would be greatly appreciated.

edit

By the way, I am reasonably attractive and am in shape and dress very nicely.

I know that sounds biased but just trust me on that
Also, I am not excellent at keeping conversation flowing, decent but there are still pauses and stuff