I always get the number by just giving her my phone on the dialer screen.

Ideally you want her to have your number too. So right after shes put in her number you can:

A) missed call/put in your info (weak)

B) text her later "good to meet you" or whatever

C) text her right then with a relevant quip (very good)

D) Get her to text herself something sexy/flirty/etc while she is still holding your phone.

I just started using the last one last night, and it was awesome! The girl is picking herself up for you and you can learn what shes into and her texting style right off the bat.

Proper tactical mate.

Edit for clarity:

Once she's put her number in and while she's still holding your phone, playfully suggest that she text something to herself, my line "Text yourself something that'll work". I enjoyed this because she basically did all the work for me while I was chatting with my friends.

In game terms, I did a nice little investment ladder,

Take my phone > Put in your number > Put in your name > Text yourself

Challenged her and got her to qualify herself to me

"Something that'll work"

And did some clean logistics (got her number, she got mine, no fuss no muss).

edit 2: I classify this as a beast at a higher level because when you're at a fancy party there's a lot of hotties to close and also a lot of business to discuss every neuron counts (being a player and being socially aware at the same time isn't always easy). With this method, she's putting in the work, freeing up your time and not making it look like you're trying to pick up. In this case we were sitting at a crowded table and she was beside me so I just put my phone on the table in front of her, screen on the dialer hand on her body so there's no confusion. I kept the story going, nobody noticed I just picked up this chick, leaving me free to get some more ;)