If you give her your number you can easily get hers. In most situations, you don't even need to ask:
"We should grab coffee/dinner/a movie together. My number is [number]; tell me your number so we can set up a time later."
Note that there's no question mark in this sentence. Say it confidently, and not hurriedly. And take out your phone and look ready to enter her number as you say it. If she has a problem with giving out her number, she'll tell you. Rejection in real life is far less dramatic than rejection in movies, as direct confrontation generally isn't feminine behavior. Then, once you have a number, don't ask when she's free -- simply propose something a few days later:
"Let's grab dinner at [place] at [time]."
If she has a problem with that place or time, she'll let you know. But you need to remember that typically women are not the aggressors in relationships -- it's on you. You have to make the first moves.