Don't make it sound like a big deal, don't make it sound like you're desperate and terrified of rejection. Don't even use the word "date".
Do make sure that you are not around her or your friends - and just casually say "hey, would you like to hang out on Saturday, maybe catch a movie or (insert other)". If she says she's busy, don't take that to mean that she doesn't want to be seen out with you (yet). Ask if there's another time when she's free and if she is still reluctant to commit to hanging out with you.....don't push it.