I found it's best to let liquor be the wind beneath your wings. Thats how I used to get girls phone numbers.
I don't think there is anything wrong with asking a girl you just met that day for her number. If anything it shows her that you are interested in her and unless you are going to see her again at another event in the near future, why not? If she doesn't want to give out her number she won't; or she'll do the hilarious "fake number" bit.

But at least you'll know. Then again I met this cute girl at a bar a while back who actually seemed interested in me and I was too pussy to ask for her number so I guess it's easier said than done.