What is it you want, here? Why? Not saying that this is a negotiation table or that it should be handled as such, but there is a lot to be said for knowing what you want before you interact.
Having a clear understanding of what you are looking to achieve gives a lot of confidence, and confidence breeds confidence. If you're confident about what you want, you'll exude that confidence, and she'll feel that. She might not be interested, but she can be confident about that. A lot of the uneasy, ill-defined, nebulous game-playing can be avoided.
That's not to say things should be mechanical; romance is kinda important. Showing some finesse is always appreciated and edifying, even if the extension is rejected. Making a note beforehand ("To the attractive drive-thru woman who I'd love to hang out with: Let's get coffee. Here's my number if you're interested.") makes it feel more personalized and invitation-like and not "I'm trying to pad things so I don't feel so bad if I get rejected".
Even better (in my book) would be to take the time to go inside and ask specifically for her. You don't need to take much time. State your business, what you're looking to do, and provide a way for her to contact you. "Hey! I'd like to go on a date with you. You're attractive and I'm interested in learning more about you. Let's do Starbucks this week. Here's my number. Call me if you're interested. I want to let you get back to being a productive employee, but I hope to hear from you! Have a grand day.
"
But despite your best efforts and preparation, being warbly and shaky may be unavoidable... but this is generally an attractive thing. I'd guess it's because it's showing to her that A.) She's got some heart "real estate" in you because you're concerned so much with what she's thinking, and B.) that she's also worth pursuing through that intense uncomfortableness.
The heart of the endeavor: Letting her know that she's worth you going out of your way for. I think that's a good foundation for any relationship.