Hey Aria..
I feel that your SO might surprise you more than you think ... If she is already accepting of trans women and she was attracted to you as a woman. I would say try not to tell her all at once, or if you do- allow her to be sad/ upset. Its a lot to process, especially if this comes as a complete surprise to her. I wasn't even openly "bi" but I have realized since my partner(ex) came out that I guess I kinda am- I've always been turned on by women as well, and just didn't really acknowledge it. Especially when it comes to her I would be ok with it. I suspect your fiancé will feel the same way. I think it is better to tell her sooner than later- and to be open to whatever emotions she feels at first. I wish my SO would have given me more time to process things. Also- try not to involve any other problems that you may be having in your relationship with you coming out to her- as I and some other people on here have expeirenced- that makes things 1000000 times more confusing and will make us feel at fault completely :-/
As for the family... I told my parents soon after my ex told me, because I love her that much. In the long run, you're going to be spending your life with your partner ideally- not your parents or hers. My parents aren't super super conservative but they also aren't hippies/ super liberal- and they kinda just took it in stride. I think it's because when they see their child as happy/ how much I loved my SO they wanted to be supportive. I think society is and has changed so much in the past 10 years or so and will continue to change and be more and more accepting. If she truly loves you and still wants a life with you she will also take this risk with her family. I had hoped that it would help my exSO feel better to know I loved her that much to share with my family/ they accepted her, but maybe it didn't matter at all.
It sounds like you deeply care for her, and if she cares for you just as much and you are meant to spend your life together, she will understand and want to be with you- especially if she's already "bi." Just give her some time to process. I hope things go well for you, and that you find the happiness you deserve.