If you're more of an intuitive storyteller, involve her with her character by asking her questions. When I introduced my most recent girlfriend
to the game, I asked her lots of questions about her character; each answer spawned two more questions I could ask her about.
Just as an example, she came up with the concept of being a warrior from a small farm. Through prompting, she invented her whole family, what they were like, what they looked like (using real world ppl for examples), what her relationship was like with each of them, and she even invented a very real grandmotherly character (which I assume was based on her RL grandmother) and I went with everything she said, inventing mannerisms and speech patterns that indentified the NPC's and differentiated them from one another.
Her first adventure entailed a small group of goblins trying to steal her father's chickens. She picked up a scythe from the shed and chased them down mercilessly. Her father, upon watching the spectacle, "reinforced" the farm implement into a 'real' weapon and off she went to find out where these goblins were coming from.
It's also very important to note that your gf may have a different learning curve when it comes to games; it's very easy to try and rush her through the 'boring' parts of rolling dice. BUT, it's very important that you explain WHY she's rolling dice and what the numbers mean.
A third idea is to create an avatar/NPC of 'yourself' in the game. I invented a warm-hearted elven ranger that helped her along in her quest by "explaining" what she could do at any point in time. For example, when she got into a fight, he explained to her what kind of actions she could do, encouraged her to try them all (ranged/melee combat, skill checks, inventive 'tricks', and so on).
They key is to be patient, remember that she's not just new to the rules, but the genre as well, and to handhold her for as long as necessary. Try not to be too fancy and impress her with scads of details; KISS simple is the best way to go. And definitely involve her in the creative story-telling. Just running her through a module is no different than doing it for the guys... in essence, she'd be pushing her pawn through the board until she got to the end. Adventures you create together will be the most memorable.