it shouldn't matter weather or not you girlfriend is converted, it's fine if you're willing to have the relationship because of who you both are, not what.
and if you are intent on having a relationship only with converted people.. it's a shame, cos that shouldn't be what you look for in love
if you want to convert her, i advise you ask her about it, maybe introduce her but don't force her. it's her choice
The answer appears simple and complex - the simple part is to do what we do with every part of our lives - submit them fully to the Creator in His Son.
Defining what the specifics will be - well - that is His job to communicate. You do not know what He may have in store for you or the other person - in the short-term or long-term - but that does not matter.
The main issue is to completely release - and be willing to deny yourself - no different than with anything else in life.