Biz cards are really cheap. You can get 500 made up for you for less than $25. Of course, you will have to use the off-the-shelf design, but for a start they're okay.
A better option I learned is to use your biz card as a mini-portfolio. With a decent word processing program and a good picture, you can present your work along with your info.
Here's the way I've learned to do it. Feel free to use this script as is, or customize it for your use.
You see someone you'd like to photograph. With your business card in hand simply walk up to her and say, "Hi, my name is Joe Smith. I'm a photographer, and I'd like to photograph you. Here's my card [extend your card to her] with my contact information. You can see my work on my website. Take a look and if you're interested, please give me a call."
Then shut up, wait a beat for her response, and walk away. I have done this about 20 times this past summer. 19 took my card. Of those 19, everyone of them was polite and friendly. Only 1 looked at me as if I were some sort of pervert, or worse, and eModel scout!
Of the 19 that took my card, 1 was interested/confident/impressed enough to follow up. I'll be shooting with her when she comes back from college for fall break.
The key with strangers -- don't oversell it. Make it quick. Make it simple. Walk away.
This is the image on my business card.
My contact info is in the space on the left.