Wow, after reading the initial question and then the latter three replies, I couldn't help but to add my say to this thread. I'm a girl much like your new girlfriend. Despite a love of books and games and intellectual pursuits, I wasn't at all into roleplaying until I happened across my husband. My experience being introduced to the roleplaying genre goes as follows. My husband, before we were wed, tried to get me into gaming by sitting me down for a one-on-one private session. We rolled up a character and then he tried to DM me through a mini adventure. That attempt failed miserably. There's nothing that will kill love of the game for a woman new to roleplaying more than feeling like a huge dork. I just couldn't get into the game with just him and me sitting around like a couple of geeks. D&D is a social event, that's why I say you should definitely NOT try to go down the "sit-her-down-in-private-for-an-introduction-to-the-game" route. Several years after the first time my husband tried to get me into gaming, he decided to start up a new group and I decided, of my own volition, to join. He basically said, "Here's this thing that I want to do, I'm going to get some of the new books, and you can feel free to join in or not." I love to read and after I finished the PHB I knew it was something I wanted to try. The key for me was that we had a group of mutual friends come over to play at our house, and that we were all having a good time together. Sometimes it's difficult to insert an outsider into a pre-existing group. The other key to my enjoyment of roleplaying was that my husband started up a new campaign. We ran through "The Sunless Citadel," and everyone enjoyed it from the longtime addictees to the newbies.
So, there you have it. No private sessions, start up a new campaign, and make sure your girl is comfortable around the other players. Above all, let her generate her own excitement for the game rather than forcing yours on her. I suggest you leave your D&D books lying around your home.