Booklady, I came out to my folks as bisexual nine years ago. I have honestly given them nine years to get used to the idea of me with a woman. Did it help? Not one bit. The whole 'we love you unconditionally no matter what' obviously didn't cover kissing girls.
I take it that your Dad has come around previously, so I trust he will this time, too. There is only so much anyone of us can do to be accepted for who we are by those closest to us. There is a time to reach out, and also a time to withdraw.
Me: bi female in my twenties