This is a pretty common scenario, so I'll get to the point. I have some conservative parents, tried to come out to my mom, and she had two responses: "You're just confused." and "What makes you think you're bisexual?" So yeah any advice on how to actually convince my mother that I'm bisexual would be amazing.
Camrok, I had the same experience when I came out bisexual/gay to my parents. My father was open and excepting, and he told me later on that he loved me no matter what. My mom was the one who reacted harshly, pushing me aside, not wanting to discuss it or even think about it. When she opened up more, she asked very similar questions to yours. You just have to hang in there, be strong. I'm hiding that I'm a young woman. Is there anywhere you can go, away from the family (for dates)?
It would help for perspective to know approx. what age you are. As far as your parents reaction, for conservative parents, that's pretty common. I wish that's all my parents said when I came out.
My parents aren't conservative and I still got this response. As long as they still love you, you can get through the awkward part in the beginning.
Arrange a threesome with a guy and a girl and let her walk in. BAM, her mind will be BLOWN. I assure you.
Ha oh you and I both.. Fun story, I actually discussed some gay feelings with my gay uncle, years ago. I was just questioning, and didn't think it was a big deal. Well he decided that it would be a good idea to bring this to the knowledge of my parents. I was like, 15, maybe. So then they confronted me and that's about how it went. Except that afterwards, I was embarrassed and betrayed, and I had no answers for them, so I just pushed it all to the back of my mind and everyone forgot. Including me, til recently.