If it terminates your friendship, she's a major bitch and your better off. Seriously, if you have feelings for her and she says no, you move on with your life. There are literally billions of fine ladies to fit your fancy, so just because one says no doesn't mean it's the end of your romantic life.
Be you. Do it away from other people, be courageous and look her in the eye, smile, practice in the mirror.
"anonymous, I want you to know something... I really like you. You're (list good qualities), and I just love being around you... Being with you is often when I'm the happiest and I feel like I can tell you anything. You probably know what I'm gonna ask... (small dramatic pause for effect because #swag) will you go out with me anon?"
Something like that. Don't get her anything, then it kinda seems like too much. If your gonna do this, do it before valentines, because valentines for pre-established couples is a +++++++. Get her a single rose, maybe cheap chocolates or a small bear. I know my second girlfriend loved the bear I gave her on valentines day (though it sits at around 2ft tall so it's kids cumbersome)
A year after breaking up, she still sleeps with it because it makes her feel safe.
So yeah, be yourself, practice in the mirror, literally no pressure at all. You got dis.
Edit:
if you decided this within a short time frame of thinking, don't do it.
You should know the person fairly well an you should be comfortable with them before you try and ask someone out. Just because she sat with you does not mean she wants to date you. If you text, hug/touch occasionally, talk a lot, she laughs at your jokes, etc, do collect $200 and pass go.
