To me, a more important definition deals with behavior. A person could find the same sex attractive but never act on that attraction. By this definition, that person is not bisexual. But by this, your girlfriend still is.
What I suspect is that your girlfriend is referring to is the romantic component. Because she doesn't have feelings for women like she does toward men, she doesn't consider herself bisexual. I don't think that any of this self-labeling versus definition discussion gets to the heart of your issues. It sounds like you simply need to ask your lady what she wants out of life and see if that lines up with what you want.

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