Holy shit. If serious have either of you actually been laid?
A physical letter becomes borderline stalking given the OPs situation. The most he can do is send an informal facebook message that says nothing he mentioned in his post other than a mention to sitting next to her once.
Yea...dont send a letter, thats a really bad idea. This day and age i think that would be seen as creepy and cowardly specially since you havent really talked with her.
How old are you and her btw? Might help us gauge your situation. I asume from this post and others your probably 15-17.
Anyway like what bananaking21 said. To break the ice send an informal facebook friend request, talk a bit and be yourself! If you can sense you and her bounce off each other pretty well then ask her out. Its unfortunite that you havent talked much and shes in a different state so it kinda limits your options.
Or you can be wild and go to her church and try to talk with her. However if you do this then you have to ask her out. Youd have to come clean and say how your mom told you about the church and that when you first saw her you liked her and wanted to get to know her more. Like i said this is a more wild approach, it does work! But you would also have to be ready for rejection.
I will say dont wait long to ask her! A crush is fine but if you wait to long and start liking her more and more it will just make it worse for you. Sad thing to say but be confident, ask her out and if she says no move on.
Remember just be yourself and confident.