I'm bi in a relationship, and I don't know if it bothers you?
You want to know if it bothers me, for real? Does being bi change anything with your relationship?
I still believe in monogamy between couples, but each person has their own orientation.
It is good to be forthright in your relationship.  Some people have different orientations from others.
I'll be honest with her since it's important to me to be monogamous.
You have the right idea about people and how to be honest even in the most intimate scenarios. That is a good way to earn your partner's trust and make them decide if they want to be with you or not forever.