If you aren't comfortable coming out to your family yet, you don't need to feel like you must tell them right now. It is okay to wait until you are comfortable enough to tell them, or even to never come out to them.
When and if you do decide to come out to them, it could help to prepare what you want to say ahead of time. If you are afraid that they will say it is just a phase, you may want to have materials written by older bisexual activists ready to show them that it is not a phase, but an actual sexual identity. Bisexual activist Robyn Ochs has written books and articles about bisexuality, so she may be a good place to start if you need research materials to show your family.
If you are under 18 and still living with your family, you may want to wait until you are more independent before coming out to them. It is unfortunate, but some teens and young adults do get kicked out of their parent's homes when they come out as LGBT+, especially those raised in more conservative families/communities.