Closeted and coming out

Ok so here is the situation, I am bi and I want to know if it's worth coming out to my family. My parents are homophobic. They told me one time they couldn't sleep in the same house as a gay couple because they thought it was so wrong. I usually stick to dating guys but I'm single right now and really would like to ask out this girl I know. She's one of my friends. She's super pretty. I admire that she is unapologetically true to who she is. I've never been confident enough to be that way and I really like that about her. Do you think it is worth coming out to my family? She would be the first girl I ever asked out. To the people who have come out, how did your family react?