I'm also bisexual, and I'm very selective about who you tell.
I know there's a big movement of "Gay Pride", and "shouting it from the rooftops" and while that's great and takes a lot of courage, it's not the only "right thing to do". For me, this feels comfortable. I don't want being bisexual to be the defining thing about me. I know people who are very forward about it and people who prefer to tell no one at all. I'm comfortable with the middle ground.
My best advice is, if you don't feel ready, don't do it. There's no taking it back. I'm not advising you to be ashamed of who you are- there's ABSOLUTELY NOTHING wrong with being gay or bi! But just like I won't walk into a catholic church and start shouting out that I'm a witch, I prefer not to tell everyone who will listen that I "swing both ways"
It's up to you. Do what feels right, when it feels right. Then, hope for the best.