My Girlfriend is bisexual. We discussed it before we got together, and we agreed to rules and limits. Luckily we both had the same basic idea, so it wasn't difficult to come to an agreement.
The rules are: she can have sex with other women, but she has to be open and honest with it with me. It would be cheating if she got sexual with a woman and hid it from me. Obviously other men are not allowed, but she isn't interested in that anyway.
I'm not threatened by her being with another girl, because I know that's just sex for her, and as a man, I fully understand how a person could find a woman's body sexually attractive. She also doesn't do that very often, so it's not like I'm competing for her attention.
She has told me that she would stop being with women if I asked her to, and I believe her, but that's not a big deal to me. It also helps her understand me too, I think. Even though she is awesome, I'm still a guy, and I still notice other girls. I don't hit on them or anything, but I do notice and look sometimes. She gets that, and isn't threatened by it (hell, she often encourages it), because she knows that I only want a relationship with her, and not these random other girls, hot though they may be. She understands that women are hot (she enjoys looking at them too), so she really gets that looking doesn't mean that "she's not enough" or that "I'm going to cheat" or any of that.
I build my relationships on communication and trust. I'm very open, and I've taught her to be too, and that only brings more security and trust to the relationship. I've had that with straight girls too, but it can actually be more difficult to get them past their jealousy and insecurity, I've found. Granted, my sample size is admittedly small.
In my experience, if you pay attention to a person's behavior, and if their words match their behavior, you can believe what they're saying. We both know that we spend most of our free time together, and that we do that because we WANT to. We have a lot of fun together, and we don't pressure each other, because there's very little insecurity.
I get that not everyone could deal with their SO being with ANYONE else. What works for me won't work for everyone, but if you are honest, open, and realistic, this isn't something that most people couldn't deal with, I think.