How do you come out to somebody that you really care about, and don't want to abandon you, but aren't sure whether or not they accept you as being bi?

First of all, remember that there's no need to rush things, coming out is something that you should only do if, when and how you feel ready. Anyway, you can tell them how you feel, explain how you realized you are bi, and what it truly means, maybe clarifying why some of the most widespread misconcepts about bisexuality are wrong, if they seem to be perplexed about your revelation. Let them express their thoughts freely and encourage them to ask you questions, if they have any. If this person cares about you as much as you care about them, if they honestly love you for who you are, it won't be your orientation to make them stop caring for you.

I'm not sure how to help you but let me try first you mite ask what there stand on it is if you want you can make it into a game and say I'm going to give you a scenario if that doesn't work just ask them what there stands are second you should probably talk about other things not just bi like maybe ace or gay,lesbian and pan maybe trans and more you don't have to this is not me trying to make you do any thing just think a little be for you do any thing just think it's the best thing to do don't jump in to anything