Women almost never ever contact the guy first. So if he does give her his number, he will never hear from her. If he does want to ask her out, he will at some point have to do it in person at her place of work anyway, unless he happens to run into her somewhere else.
There's a fine line between creepy and assertive, and it takes some social awareness to walk that line. She can reject him either way, and he has to convey an attitude that he'll be respecting of that. Being honest and up front, while being respectful of the other person's reactions, is the opposite of being creepy.
Be direct, but convey that you are aware that what you're doing isn't "normal," convey that you realize she's at work so you want to be respectful of that, convey that if she says no, you'll respect her decision.
This sort of attitude took me far in dating. I'm not trying to portray myself as some player, because I'm not, and being with many women isn't a virtue IMO anyway. However, I lived a phase of my life being the typical anti-social, awkward loner who couldn't get dates to save his life, then I lived another phase where I was meeting more women than I thought was possible for me. Learning how to take control of this particular realm of life is a big step towards a better life for many young men, so I encourage a more assertive approach.