Most Helpful Girl
I am bi and always let guys know I am before I enter a relationship with them. I had a boyfriend who became insecure although he was fine with him in the beginning. His insecurity ended up affecting the relationship much more than my bisexuality. He became paranoid with girls too and I felt trapped in a cage. The questions you should ask yourself is "can I trust my girlfriend to not cheat on me (in general)?" and "does her notion of cheating also extend to girls?". As long as you are clear about it, you'll be fine. I'd suggest you talk to her about your concerns. You could start saying "I really appreciate the fact that you were honest with me about it, I very much admire your courage in expressing who you are and I am totally supportive of you. Nevertheless, I am a bit insecure about myself now because I have never been in this situation before, I do not know how it works." and you can keep going asking her questions that can end your doubts. To conclude, I can tell from experience that when you love your partner, you do not cheat on him. It does not matter what gender you might be attracted to sexually. And she is not going to find every other girl attractive just like you do not find every girl you cross attractive. She might even prefer men to women. Sexual orientation is not all black and white, it has maaaany shades.
Most Helpful Guy
What is the insecurity? that you can't satisfy her and she'll need a woman for that? that she'll leave you? that she'll cheat on you with another woman, or fall in love with another woman more than with you? that you've lost a well-dressed gf?
Maybe ask her where's she's going with this. Tell her you don't want to lose her, or what insecurities you have. Be open. She was.