So, that is normal, is bisexuality. I was 15 years old when I fell inlove with a girl. And my thoughts was like "Wtf, I am inlove with a girl, that is wreid"
I had alot of hours of thinking about it, and understood, that this girl is too important to me. I told to her about my feelings, and we were together.
Bisexuality - is not terrible thing. You just love a person. Person, which understand you and you don't feel empty.
So, what about parents, just don't tell to them. They may not understand that. Just live with your feelings.