Disclaimer: Don't get mad at me. This is my best answer and I'm not trying to be offensive or hurt anyone. I'm seriously just trying so help because that's what the author said she wanted. I hope you understand where I'm coming from.
In the Bible, being gay or bisexual is a sin. Also, cheating, stealing, etc are sins and if you are religious, you should already know that it's human nature for us to sin. There is no sin that's worsethan any others. Sin is sin in God's eyes. In no way did God say, "Hate gays and bisexuals. THEY ARE BAD AND I HATE GAYS." It would be the same as God saying, "I HATE ALL SINNERS!" For anyone who thinks being gay is the ultimate sin and all that, that's BULL SHIT. Also, please don't let being bisexual interfere with your relationship with God no matter what people say.
To be realistic, there's no "good way" to tell them. If they're as religious as you say they are, they won't be okay with it for a loonnnggg time-no to put you down. But, if your parents love you and care about you, they will try to understand you. Although it may take time for them to understand, wait for them. Don't hate them if they react badly, it's just because they love you and they don't know how else to react.
I hope you really don't get offended by this part, but if you do, I apologize. But please make sure you're not "choosing" to be bisexual. If you really feel that you were born that way, then I understand, but if you're attracted to guys also, chances are that it's just a stage or you overthinking yourself. Are you sure you were in love with the girl or did you just love her in a friend way? If you really think you can't help it, I get it, but also just rethink yourself before you make that big of a decision.
Also, when you tell your parents, I think you should tell the one that you're closer to and maybe they'll understand better and explain it to the other parent in a better manner.
Hope I helped!!!