I just started dating my girlfriend this week, but at our very first date, I brought up my faith and discovered that she is an agnostic. I assumed she was a Christian because she is a very nice girl and a hard worker (I work with her at Pizza Ranch, which also happens to be Christ-affiliated), and I know for a fact that she has never had a boyfriend before. She said that she wants to believe in God but has trouble believing ins something that she cannot empirically touch. I tried to share some apologetics, and she is actually kind of interested in my faith, but she still has a lot to go before the Holy Spirit convicts her. I made it apparent that it will become a problem if neither of us changes - and I'm not giving up my Christ for her. I tell her I pray for her, and I make sure that I remain consistent in my faith so that she may see the Truth in my actions and heart. Unfortunately, I accidentally made a blunder last night when I texted something that unintentionally insulted her agnosticism. I immediately apologized, and next time I see her, I will give her a flower.
What is more important than your relationship with her is her own relationship with Jesus, and if you can postpone your own relationship with her (of course, still remain friends!) until she decides to have a personal relationship with Christ. I told my friend that I will never kiss her or even hold her hand until she becomes a Christian. This protects ourselves if we do end up breaking up, and it shows that I genuinely value her rather than wanting a girlfriend for whatever other benefits may arouse.