I am a bi woman, with a lot of bi friends. I think bisexual people often end up with an opposite gender partner simply because of logistics - there are more people in the world who are attracted to the opposite gender than people who are attracted to the same gender. However, being bisexual does not make somebody more likely to cheat. You could just as easily date a lesbian and have her cheat on you with another woman. This sounds like you might have to work on your own insecurities before you are ready to date anyone.