Coming out to my best friend...resulted in us realizing that we both are poly! I've come out to one polyfriendly coworker and she literally had such a positive reaction (she reacted as if it was literally the smallest deal ever) I made sure she knew I wasn't joking! It was actually pretty awesome to have someone give so little shits and treat it as if it's super normal. We don't try to hide things from our neighbours.
For us, it's my mom that is the barrier to being open. How does one deal with a wildcard?
1. Think about what you know of her. What is her background, is she easily threatened by "different?" Is she fairly open-minded? Have you heard her say judgmental things about others? What are her politics? Her religious values? Are her hopes for you more that you will do objectively "good" things (achievements) with your life, or that you will be happy? How concerned is she with appearances and impressing others?
2. Based on how you poly, and how involved (or not) she is in your life, is it even important for her to know? Would she find out if you didn't tell her? (If the odds are she'll find out anyways, it's probably best to tell her yourself.)
3. Are you prepared to explain how you poly and why it contributes to your happiness? Do you have skills in being diplomatic in presenting new ideas to other people? A lot of things come down to how you say it, rather than what you say. Being able to connect with others on levels that mean something to them is a gift...not everyone is good at it.
And sometimes, a wildcard is a wildcard and there is no predicting it.
My little brother is very, very religious. But...in kind of a cool way. He is not very judgy, he has traveled on mission work, but this is building homes and planting gardens for the poor. He plays his guitar and sings about Jesus and smokes a pipe. He's kind of a hipster/bohemian who is all light and love, and Jesus and God's plan and stuff.
I...am a former Satanist, a masochist, a hedonist, and well...he's got every reason to fret about my soul. Or...whatever.
We get along great. And I was easily able to explain my involvement with BDSM in a way that he totally gets. He has been into rock climbing, and kayaking and other high-thrill adrenaline activities, see. I'm only getting high on the chemicals that God gave me. It's more a matter of meditation and transcendence through pain, than it is weird sex. And he totally got that.
My Mom on the other hand, is freaky in her own way, not religious at ALL, and very very liberal. She didn't judge me when I was a pot smoker (many years ago) and she didn't judge me for being an "ethical slut" flavored solo poly sort of a gal and she wouldn't judge me if I chased sex or money or whatever. But BDSM? Suddenly she is protective and doesn't like what I'm doing. What...?
Point being...yes, you can think this through and come at it all prepared and imagine you know what to expect from people, and yet they can still surprise you. Which brings me to my final point:
4. What happens if she reacts badly? What are the stakes, before you throw the dice and tell her, what do you stand to lose if she freaks out?