Who do you consider the schoolyard bully in your situation? Your girlfriend or the men she is with?
I am in much the same type of relationship with my wife. I am happy with her having another significant other and feel I am more mono, but it all works good. Just like you said, I enjoy the thought of her with another guy and often get off on the thought of it. If there is ever a time when I am feeling a little bit jealous of her with someone else, I always remind myself of what I get from it as well as what she gets from it as well and that feeling always passes. She is not into the idea of having a lot of men, but actually having a relationship with one guy and that guy committed to her only, hence being poly. It works for us and we are both very happy with were we are in our relationship and how a third brings something new to the relationship.
Hopefully things will get better as you better understand your wants and needs in addition to your girlfriends wants and needs and how you both can benefit from them. It can work.