Yeh, there's no easy way to put it. You have to overcome your fears of social interaction on every level. You need the self belief to be able to say whatever you like to anyone you like, and to know that you can control your interaction with them so completely that you will get the result you are aiming for.
I know it sounds silly, but at the end of the day, the only girl that would want to date a girl is a lesbian. So unless you are trying to pick up lesbians, you need to be a man.
There is no right and wrong
thing to say when asking for a girl's number. There is a right and wrong
way to say it though. Every famous mPUA you have ever heard it, be it Ross Jeffries, Style, Mystery, Lovedrop, Matador, Tylerdurden... all they try to do is to model the behaviour of "naturals".
"You should not directly ask for a number." Is just a conclusion that has been drawn as a general rule. In my experience, that is only a partially correct observation. Each girl is different and each interaction you engineer is different, and each interaction therefore has its own rules.
I know some girls who would not give their numbers to Casanova himself if he didn't directly ask them for it. On the other hand it is a good indication that you have done well in your sarge if the girl offers it to you without too much hassle.
I should write a book too
S