Apparently this still goes on. In today's New York Times there's an article called Forget the Vespa: Making Your 2 Wheels a Bike in Rome.
“Bike riding has gotten more popular due to the city’s antipollution politics,” said Alessandro Piccione, a Roman engineer pedaling along the Tiber immaculately dressed (of course) in a blazer on his way to work. “I don’t just bike working days, but weekends, too. It saves a lot of time and trouble parking.”I sometimes feel bad about wearing cycling-specific clothes to ride to work, then changing, when the cyclists in Amsterdam and Copenhagen manage to get along looking normal and even downright fashionable. Days like today I could wear my office clothes, but soon it'll be too cold and not long ago it was too hot. In the meantime, Rome sounds a treat off a bike.