I would make sure that u are positive about it! I know that u may truely believe you are now but why is it imperative that you tell her? I mean ultimately your going to choose to date someone be it male or female and she can find out than! But until than I agree with the answer that you can see how she feels about it by telling her that one of your friends is bi and see how she reacts to it. And you could always drop hints and let her figure it out!
Ok my question is this have you been with someone of the same sex or are you just curious about the same sex? If you are only curious why tell anyone anything until you have explored and know you enjoy sex with someone the same sex!
take it from someone who went through this! as ridiculous as it may sound, tell her that you're fully gay. i know it's a lot harder but when you say you're bi, it'll always be like..why aren't you dating a guy huh? she'll discourage you from dating any girl you have feelings for, thinking that you have a choice. i went through it, i have friends who went through it..and we all regret not having thought of this sooner. if you're gay, there's nothing she could do about it, you were born that way. she couldn't do anything about you being bi either but she'll think that she can. it's a lot to take in but eventually she'll get over it. good luck!