I believe at least two major retailers (including WalMart, I believe) have been sued (and lost multi-million dollar verdicts) by various photographic studios for not having aggressive copyright protection policies in effect at their stores.
Copyright infringement laws don't only protect those big, bad giant retailers. They also protect the thousands of independent studios and photographers who rely on their photography for a living.
Most of the retailer rules focus on any image that appears to be a "professionally" taken portrait or portrait-style photo. Admittedly, this is the area that often causes dispute due to the judgement being made by an hourly employee at the retail location. However, they are trained to be overly-cautious and to err on the side of not letting the photo be copied.
I don't believe a business card will do the trick. The best thing would be, as was already suggested in this thread, to print out a release form (examples can be found online) with a '"YOUR NAME HERE" PHOTOGRAPHY" style letterhead. The retailer may want a phone number to call for verification and make a copy of the release to keep as proof of having seen it.
As casual, serious amateur or semi-pro photographers, we may not know why there is a need for copyright protection or why we aren't allowed to print our own pictures at a retailer. But any and all true professional photographers as a whole know and appreciate the rules and would expect the retailer to stop them. If they, in a pinch, ever need to use a retailer to print their own stuff, they know to bring a release - and will probably lecture the clerk if they don't ask for one.