I often ride with my wife, and she knows I'm twice her speed. Most of the time I just relax and spin away, but when she knows the route or path I'll do lots of sprints a mile out ahead of her, turn around and catch her and ride slowly to recover. Viola - instant intervals!
Sometimes when she wants to work on her speed I'll set a "pace" for her that she has to keep. Good training for her as well.
But I'd never do this with a new cyclist. It's rude. What's your girlfriend look like - maybe I can help her out a little?