This doesn’t need to be followed verbatim, but every element serves a purpose.

Suggest an activity to do with her.
When she says yes, say, “Right, do you have a cell?”
Type her number into your cell.
Ask, “Do you have Caller ID?”
When she says yes, say, “Okay. I’m hitting dial - my number will show
up on your screen.”
Wait for your number to show up on her screen, then press end. Don’t
hold the phone to your ear while calling.
Spell your name for her, especially if it’s a generic name.

Sounds like a lot? It’s really simple, but every element is designed
for maximum effectiveness.

It looks like this:

“There’s a cool gallery opening up soon. We should go.”
Her: “Okay.”
“Right, do you have a cell?”
She’ll nod or say yes.
“Okay… 212…3444….4444… Do you have Caller ID?”
She nods or says yes.
“Okay. I’m hitting dial - my number will show up on your screen.”
It does (her phone starts ringing - if it doesn’t, try again. if she
says, “Oh, my phone isn’t on me/it’s my home phone/etc” it’s a bad
number and throw it away after you’ve left her company)
“Cool. Now my name is spelled just like it sounds. B-O-B.”

A few key points:

You’re making the focus doing the activity with her; not trying to her number (that’s why you suggest an activity first).

You ask, “Do you have a cell?” - You don’t even MENTION the word “number”, which has a bad rep and potentially sets off player alarm.

Caller ID ensures she has your number. That means she’s more likely to answer if she likes you (you were in trouble anyway if she doesn’t like you, and girls are less likely to answer unknown numbers - MUCH less likely).

(as an added bonus, if the number is fake you’ll know right away, though you’ll find that happening less and less)

You spell your name in case she’s forgotten it.

Solid formula. You’ll never hear, “I don’t give my number out” if you practice like this. Then remember: The first step after getting her number is to text her before you ever call. Text her within 24 hours if you met at a nightclub, within 48 hours if you met in the daytime. Texts should be friendly; first texts should never tease, bust, or insult unless you had a dynamic that was strongly like that. Stress friendship when you text. “happy to make friends with u :)” is not a bad first text.

Have fun!

Sebastian