Much better to just whip out your cell phone and ask what's her number. Type it into yours as she gives it to you, and ask how she spells her name. (Helps in case you just forgot her name.) Then call her right then and there and see if her phone rings. And say "now you have my number -- I spell it..." and spell out your name. If things are going well, click a photo of her face to put in her contact. After you leave, type in a couple of notes about her and organize her contact into the proper group.
Taking a little time and effort tells her that you're not some pick up artist who goes around getting the numbers of ten new women a day.
Business cards? Hmm. The usual trick is to pull out a fairly bland, standard business card, and say "but let me give you my personal number," and write that on the back. If you're not allowed to get personal calls at work, or if you share lines with coworkers who aren't helpful about such matters, you'd pretty much have to do it this way. You'd better not try to present yourself as the boss (why wouldn't you be able to get personal calls at work? your busted-azz business can't afford call forwarding?).
I've seen hundreds of calling cards that players hand out. Women love the remembrance of being hit on. They carry them around for years in their cars and purses. And leave them on the dresser or nightstand next to the bed. I always equated that with a woman leaving a condom or its empty wrapper in similar places. They get these things from men who are promoting hypergamy from the position of being external to, and trying to break up, other men's current relationships.
Really, it's more honest all around to just ask for a phone number. You present yourself as a single man who wants a single woman -- not as a sleezebag who's asking her to cheat. If she doesn't give you the number, she doesn't like you, she has a man and he'd be pissed off if she starts getting calls from you, or so on. Not giving you her number is an excellent indicator that you're still too much of a stranger to ask, or that she's not available.
What man asks permission of the father before courting a girl? The simple courtesies "May I?" and "Will you?" never cross one's ears -- permissive authority has been so usurped from man by the state.