I am a 32-year-old lesbian who has a 26-year-old lover who says she is bisexual. She tells me that she is happy in our relationship, our sex life is good, but that she needs to be with a man now and then. I am not comfortable with this, and am very uncomfortable with the thought of her being with a man, especially as I suspect it's the same guy each time (I suppose that's better than her sleeping around with a whole bunch of guys). She sees this man every two weeks or so and says it's only about sex, but even if that's true, I do not want to share her with anybody. She says I am close-minded. I love her, but I am just not comfortable with this arrangement. Suffering Sappho.
And why should you be comfortable with this arrangement? If you want a monogamous relationship -- which does not in any way make you "close-minded" -- you should be with someone who believes in monogamy, and it doesn't matter what her sexual orientation is. I personally have nothing against open relationships, but both parties should agree to this -- if not, then one of them is cheating. You should make it clear that this arrangement is not one you can live with; you are not giving her "permission" to cheat.
Besides, bisexual advocates (with whom I do not always agree) argue that it is a stereotype that bi's need to be with both men and women on a regular basis -- only that they can fall in love with either a man or a woman. They also argue that bi's are not more inclined to be unfaithful than gays or straights. Perhaps your lover is also (or only) sleeping with other women, and is using the bi business for a convenient excuse, figuring you'll find the idea more palatable if you think, because she's bi, that she has to have both men and women. Or perhaps she's dealing with internalized homophobia, and sleeps with men to feel more feminine or "normal." I also sense that you fear -- if she's seeing the same man (sort of a "male mistress") on a regular basis -- that she may develop feelings for him and leave you, which is certainly a possibility.
In the long run, it doesn't matter if she's bi or gay or whether she's seeing one man, many men, other women, or both. She's a "swinger" and you're not. Sit down with her and tell her you want a monogamous relationship, and if she's not comfortable with that, then perhaps it's time to move on. Maybe if you make it emphatically clear how you feel, she'll come around, but she could always keep cheating behind your back. For her, her bisexuality could be a phase, but on the other hand she may never want to give up men, for whatever reason.
What's the point of holding on to a relationship -- no matter how much in love you may think you are -- if it just causes you doubt, confusion, and unhappiness? It may be painful, but you're young and there are other wonderful women out there who will be happily satisfied with you alone.