I talked to her a bit on the phone, and just struck up a conversation with her, but didn't bring up what I wanted to tell her but that I'd call back later because I figured she should be at home and not in the middle of the commissary on base when I told her this. She called me back as soon as she got home. I explained that, "Before I tell you this, I need to make 3 things very clear to you."
I don't remember my exact words, but the list I wrote on paper was:
1. I'm terrified to admit this.
2. I know that this is going to be completely out of the blue to you, and I apologize in advance.
3. This is a real, legitimate medical issue, and isn't what's probably going to jump to mind when I tell you this.
Then I took a couple of deep breaths and told her.
She didn't even take three seconds to tell me that it doesn't change how she feels about me, and that while she doesn't know much about it, she has heard about trans people before at least, and she was aware that our lives can be rather challenging. I don't really remember the rest of the conversation really, but she was very supportive, and has offered to help me figure out how to break this to the rest of my family.