In my Chinese class we haven't really discussed how to ask people for their number, only business cards "Zhao pian" what would be the proper way to ask a girl for a number? I am thinking "wo keyi you shu" with the vocabulary that I do know.
I assume you want ask number for dating purpose.
I don't think this is a Chinese language problem. The difficulty is not how to ask but when to ask.
"number" should be translated into "号" but not "数" here.
You may say "我能留一下你的手机号吗？"(May I take down your phone number?). However, the more popular way in China is to ask their to add your WeChat(http://www.wechat.com/en/).
Nowadays Chinese girls prefer using WeChat to making phone calls or texting. I recommend you to install this popular app and tell Chinese girls "加我微信吧" or "你微信号是多少？我想加你".
lit. leave a phone (number) - but it means the same as 'let me get your number'.
电话 means phone but can also mean phone number by extension - 号码 means number as in phone number, house number, etc. but that's optional here (hence the parenthesis above).
'shu' (数) on the other hand - as you wrote above - means number as in 1-10 but cannot be extended to other things.
So you could say: 美女，留个电话 but maybe you should be asking for their weixin (aka. wechat) instead...