have you tried going out to dinner with just her parents? I don't mean like to make a deal or anything just to get to know you better. Treating them to dinner would be an even better Idea.
I am 16 and my girlfriend lives far away too. I get to see her once a monthish. the only reason it remotely works out is from trust on both sides and the fact I can fly a plane there helps a whole lot. So far a year and some change and thats just been since it was official. I only keep track of the years
One more thing, stop saying you don't want sex. I am a faithful Christian and I want sex but I am waiting for marriage. It doesn't change that I don't want it or don't think about it. I can just control it.