One way Love, only chance has us meet.

I adore this girl that I rarely see, but when we are together we just 'work'.
I have worked out that we only become 'cosy', even at get-togethers, by chance. i.e. She is moved next to me in the room. So today me and my friend (recently going out with somebody) had a movie night at his (with his said girlfriend too), coaxing the girl I like along. Now here is where it gets complicated:
I am not social, I will not just go and sit next to her; a real big elephant is always in the room. So today I spent 5 hours on another sofa 2ft away from her (-.-)
Once I am next to her we just become I-have-no-idea, but in a good way.
What I need answering is (all to do with a next, unplanned movie night):
Do I have to break my 'barrier' and become relatively social to get her next to me and me next to her? We are not going out and, when joked about we should, we both quickly say 'no'.
Basically, very long story, known each other for ages, but never see each other often.

Oh..... And she is the only female friend I have, and it is 'annoying' that I am not her only male one (I know it is selfish but, put your self in my shoes)
Any other advice would be great too! Seriously, I am so socially confused; only need help with this however.

You don't have to be social with others but if this is going anywhere you have to get social with her.

Spend as much time with her as you can. If there is any chemistry there, it will develop. Watch her body language. When you move closer into her space does she move toward you or away from you? If you take her by the hand, does she hold on or jerk away? If you hug her, does she hug you back? The way she reacts to movements like that will tell you more about how she feels than chit-chat.