Well, you have a choice here. There is a huge potential risk in telling your religious loved ones (they'll freak out, retaliate) and very little potential reward (unless you are in a relationship that you are actively having to hide).
If you think that same-sex relationships are going to be a part of your future, then I would plan on atleast telling your parents. Just bite the bullet, be direct, and be understanding if they freak out. Lots of parents have a bad reaction but then come around. However, if they are supporting you financially, I would wait until you are financially independent to tell them.
Bisexuality can mean different things for different people. Some bisexuals have the capacity to have sex with both men and women, but only fall in love/have relationships with one or the other. If you are capable of same-sex attraction but only have opposite sex relationships, I would think carefully about telling your parents. If this identity only goes as far as the bedroom, they probably don't need to know.