Everybody wants to feel special in a relationship. Your girlfriend isn’t hurt at guys hitting on you. She’s hurt because you’re forcing her to be in the closet with you. I don’t doubt she understands — you’re not ready to come out. And coming out is a big decision, and a brave leap. It’s declaring who you are to a world that will embrace and reject you.
Heterosexuals don’t have to be quite so courageous with their identity.
I would talk to someone who has gone through what you’re going through who is not your girlfriend. Because I can’t see your relationship continuing much longer if one of you is out and one of you isn’t, There’s going to come a point where your girlfriend is going to have the right to expect a relationship where she doesn’t have to live a lie. Where she can be proud and public about her significant other.
That said, all you have to say is “no.” You might have to say it over and over. But if you don’t want to be rude, and you don’t want to admit that you’re dating a woman, then you’re just going to have to repeat yourself. Guys can be thick sometimes. Which is why you’ll have to be repetitive.
Just keep saying “no” with a smile. Eventually, the dudes will take the hint. It just might take a little while. In the meantime, I hope you can find a mentor who you can talk to about your sexuality. It sounds like you have feelings for your girlfriend. You need to start getting to a place where you are comfortable sharing the good news with the world.