Wouldn't you rather have a nice cup of tea?
I was actually in this situation once. Dated a bi-girl, but she wanted to continue sleeping with women, and said that asking her to be in a monogamous relationship was like denying half of her sexuality, and she couldn't be happy that way. But I couldn't be happy without monogamy. So if neither of us could really be happy in a relationship, it made sense not to be in one. We broke up after a few months.
Don't believe everything that you read.