Bullet Train from Rome to Sorrento

Technically speaking there are no bullet trains in Italy.

No. To get to Sorrento by rail, you'd take a fast train from Rome to Naples' central station ("Napoli Centrale"), where you'd then transfer to the local "Circumvesuviana" train which takes you to Sorrento.

There are plenty of bullets flying around Naples, courtesy of the Camorra, but no bullet trains between Naples and Sorrento, only a commuter train run by the Circumvesuviana (www.vesuviana.it). There is a high speed train from Rome to Naples. For schedules and prices go to:
www.trenitalia.com. Once in Naples Central station go downstairs in the underground station where the Circumvesuviana trains arrive. Take a train to Sorrento from there.

Sorrento is the last stop on the Circumvesuviana line, it takes a little more than an hour to get there from Napoli Centrale (also called Stazione Garibaldi).