I think it’s time for you to move on because your girlfriend is interested in men, and there is no way, as a woman, that you can satisfy that need. This is aside from the fact that she cheated on you. If you accept her apology and expect her to remain monogamous, you’re fooling yourself. If she’s going to want men in addition to women, you’re only ever going to be able to satisfy half of her needs — through no fault of your own. So accept reality, and know that your girlfriend isn’t right for you.
You may think you’re in love with her, but she’s just disrespected you and hurt you a lot. That’s not how a lover or a friend acts. Understand that just because you love her, doesn’t mean she’s a compatible lover or girlfriend, and you can do a lot better by finding someone who is respectful, monogamous, and as into you as you are into her.
I hope that helps.
Good luck, and let me know how things go.