I have two bits of advice:
1. SMILE
2. Make eye contact
Eye contact is everything! When you look into her eyes, you display confidence and also the fact that you are interested. Look away, or look at the floor, and you've made a big mistake.
SMILE! I think perhaps you're taking this too seriously and are acting stiff and nervous because of it. Smiling lets her know that you could be fun to be with, and not boring. Girls don't like boring guys. I know firsthand about that.
Walk with your back straight, slowly but calmly. Smile, look her in the eyes, demonstrate interest in her, and display the utmost confidence; otherwise, she'll think you're just a "kid" and move on to other things (which she might do anyway).
But have hope; you could make some serious headway in two months if you do it right. And from what you say it sounds like she does like you for one reason or another, so it'll be a little easier than starting off cold.
Good luck!