The coach was taking about 50 people, including children, back to Naples following a pilgrimage.
The cause of the accident is not yet known. Some reports say the vehicle was travelling at speed.
The head of the local fire brigade division, Alessio Barbarulo, said barriers on bridges would normally prevent such accidents but "evidently it seems the impact was so strong that even the barrier gave way".
A survivor said the driver, who was among the dead, appeared to have lost control of the bus, possibly after a tyre punctured.
Transport Minister Maurizio Lupi said the vehicle had passed its annual inspection in March, and there was no indication of technical problems.
Tests are being carried out on the driver's body as part of the investigation into what caused the accident.
The crash took place in the mountains some 50km east of Naples along the Autostrada A16- a toll highway linking Naples with Canosa di Puglia on Italy's Adriatic coast. Some of the hospitalized include occupants of the cars that the bus struck before crashing into the guard rail and going over the embankment.
This week's crash is even deadlier than last year's Costa Concordia shipwreck off of the Isloa de Giglio off the coast of Tuscany. The captain of the vessel is currently undergoing trial in Grosseto, Tuscany on multiple charges of manslaughter and abandoning ship.