Yes, this is/was a very famous con, perhaps the canonical example of a swindle, and was perpetuated frequently in the streets of turn of the century New York. Here's a great NYT article on the con. Money quote:

Since the bridge was completed in 1883, the idea of illegally selling it has become the ultimate example of the power of persuasion. A good salesman could sell it, a great swindler would sell it, and the perfect sucker would fall for the scam.

But this was not just a rhetorical or a fictional conceit. A turn-of-the-century confidence man named George C. Parker actually sold the Brooklyn Bridge more than once. According to Carl Sifakis, who tells his story in "Hoaxes and Scams: A Compendium of Deceptions, Ruses and Swindles," Parker -- who was also adept at selling the Metropolitan Museum of Art, the Statue of Liberty and Grant's Tomb -- produced impressive forged documents to prove that he was the bridge's owner, then convinced his buyers that they could make a fortune by controlling access to the roadway. "Several times," Mr. Sifakis wrote, "Parker's victims had to be rousted from the bridge by police when they tried to erect toll barriers."

Another seller was William McCloundy, also known as "I.O.U. O'Brien," who sold the bridge in 1901, "for which he was convicted of grand larceny and served two and a half years in Sing Sing," The New York Times wrote some years later.