Oh boy do you sound like Mono
. He struggled with my sleeping with other men too when we first began and it's been 20 months now. Perhaps doing some reading of what he went through at the beginning would be helpful. Or at least sending him a PM about it? He could at least support your worries.
I can imagine that it would be very hard for many people to come to terms with the fact that their loves want and do have sex with other people. I would suggest that perhaps you look at what sex means to you... do you feel that it is a ways to increase a bond and connect? Or is it just a fun activity? Is it different with different people and how can you have fun or connection without sex? Then ask her what her opinion is... if she is bi then she will feel similarly about sex with men AND women. How can you use what you know about yourself in terms of the differences you feel there are in such a way as to re-think your dilemma?