You must keep in mind that a dog does not miss a bite or fail to break skin by accident. She didn't break skin because she didn't want to break skin. It is a lower level bite, but a bite nonetheless. First place yourself as head of the household, then place your girlfriend as number two. Pepper will be resistant to this at first, but once she sees she does not rate as high as your girlfriend, she should settle in.
One way your girlfriend can help make this happen is to "take possession" of something Pepper has. A spot on the floor, a toy, whatever. She does this by calmly and without saying a word, just step in slowly on the place/item until Pepper gets the idea and moves or gives it up. Edge in and wait. Do not look Pepper straight in the face: that's a direct challenge. Just move in and take whatever it is you want. Once Pepper realizes she has to move for the girlfriend, she will start to get the idea.
I wouldn't start this exercise with space around you just yet. If your girlfriend wants to sit down, I would suggest you move Pepper rather than make your girlfriend do it. Start with places and things that your girlfriend can "claim" without using her hands. Eventually, Pepper will see her as a leader rather than a rival bitch. (No offense meant at all to your girlfriend.)