Yes, the best way to do this is to create your game and starting characters on your xbox. At this point you can play together at your place. If she goes home she can continue playing with you by joining your game and taking control over her character again.
Also if you ever break up you can still finish the game since you can control her characters as well, but let's hope that never happens :P.
Awesome guys, thanks for your response. And I'll be sure to tell the the last part