Being bi does not mean you have to actually have sex with both men and women. In my opinion, it comes down to two aspects of attraction: whether you are emotionally attracted to one or both genders and whether you are physically attracted to one or both genders. To be bi, you would at minimum have at least one of the two aspects of attraction for men and at least one of the aspects of attraction for women. You do not need to have had sex with both genders to be bi. Therefore, a guy can have sex with only men and still be bi.
Further, a bi guy can equally be in a monogamous relationship with a guy as can a gay guy. Some gay men have trouble dating bi guys because they think bi guys can't be faithful and will cheat with women. But a gay guy can just as easily cheat with another guy when in a relationship with a gay or bi guy.