Coming out is usually pretty tricky, especially to someone you care about. Every coming out situation is different in their own way so there isn't a right or wrong way to do it. The best thing I can tell you is to prepare yourself with what bisexuality is and what it means to you so that you can explain things to her in case she doesn't react well. You'll have to dig deep into yourself and ask yourself why did you decide to label yourself as bisexual (it's different than deciding to be bisexual because that's not a thing however choosing what to call yourself is a choice). It's best to try to understand what bisexuality means to you first because I find that it's easier to explain what it is if you know the significance it holds in your life.
You should also touch on countering common misconception of bisexuality. For one, bisexuality does not mean that you are greedy and want to have sex with everyone. It just means that you can have a crush on either someone who is male or female.
Another misconception is that bisexual people are confused and they can't choose whether or not to be straight or gay. First off, sexuality isn't a choice so there is no choosing involved. Second of all, what's wrong with liking more than one sex? There is literally no significant advantage or disadvantage for liking more than one sex so why should it matter? Why must everyone be so concerned with liking one type of sex?
And lastly, some people think that bisexuals are always okay with having polyamorous relationships and threesomes. Even though there is nothing inherently wrong with those kinds of relationships and sexual activities, it isn't right to assume that one's sexuality will determine if that's what they're into. There literally is no connection between sexual habits, relationship choices, and sexuality except for the sex of the people you get involved with. It's as ridiculous as assuming that ALL gay men want to have open relationships or that ALL straight women like missionary. If you're bisexual and that's what you're into, that's great. But if not, then that's perfectly okay too and people should respect that.
However in the end if she still doesn't like it after explaining what it is and all its misconceptions, you should give her some space. For some people it's hard for them to accept something that they may not understand and leaving them alone for a while could help them process it. You did all you could do at that point and there would be no reason or good way for you to try to press her and convince her why she should accept it.
The best scenario to happen is that she doesn't care that you're bisexual and that she is supportive of you and I really hope that this is what happens. But we can never be sure. So with those things in mind, that's all you can do to prepare for what's to come next. I hope that she'll take it well and good luck!
