My friend is not really supportive of me

I really like her, and she me, We're good friends. But, i've been questioning for awhile, and she has been bi for years. I started talking to her about possibly being bi awhile ago and she got really annoyed, thinking i was faking it. I talked to her recently as well, when she asked me what my orientation was and was just annoyed at my response. For weeks, she was just angry at me. She is a good friend to me, but i just know, no matter what, she'll probably be mad at me for awhile if i come out as gay, let alone bi. How do i make her more accostomed to the fact that i'm not saying this stuff to her for attention, but because this is generally what i'm actually mulling over.
I know that she'd be very supportive of me, like she has been for many other people who have come out if she knows i'm not faking. But i don't know how to convince her of that.
Any help would be appreciated.