You don't mention your age, and age is very important. If you are under 18, there's a chance your sexuality is still developing (some will even say it is still developing beyond 18!) Telling your family you are bi is a big thing, and you want to be 100% certain. Secondly, if you are still living at home, and people you live with are the ones who's reactions you worry about, again you can end up making your life difficult by saying anything at this stage. After all, you have to live with them. If any of the above sounds like you, allow yourself to enjoy being bisexual without feeling the need to tell your family; your sexuality is your own and you don't owe anyone any explanations!
If, however, you are standing on your own two feet, either at uni or working, and living away from home, and you really feel strongly about 'coming out', perhaps it's time to let the world know who you really are? Keep in mind, very rarely will everyone be happy about this sort of thing. But hopefully, with time they will realise that your sexuality has nothing to do with them; you are still the same person they loved to death before they knew this. And the ones who can't get over it? It's sad but not everyone is destined to last a lifetime with you, even close friends and family. Let them go without bitterness, and think of all that space freed up in your life to meet all those fantastic people you've yet to meet, people who will adore you for who you really are!