Well, apparently, they have.
People magazine is reporting that a spokesperson for the couple said "the Duke and Duchess of Cambridge occasionally use the London cycle scheme bicycles to undertake private journeys around London."
London's bike share program began in July of 2010 and has proven to be enormously popular, with 7.7 million bicycle rides taken to date.
Apparently -- and, on behalf of TN, I apologize for missing this tidbit when it came out last spring -- the Mayor of London, Boris Johnson, gave the royal couple a specially built tandem bicycle for a wedding present. (There's no word on whether the couple has actually ridden their tandem, or just grabs a Boris Bike from one of the 400 docking stations around town.)
You can see an animated video of it, below: