Siena to Sorrento

It's a long trip. Although crowded in both places, you are going from one geographically rural area to another. Much of your journey will be on local Regionale trains that stop at every station. There's nothing fast about it. You're looking at 7.0hrs minimum. By train, half the runs backtrack to Florence to put you on a Eurostar-Alta Velocita to Naples. The fare is 69.90Euros. Or, you can take the local train from Siena to Chiusi and transfer to an IC train to Naples. The trains are older but the trip is a bit faster and the fare is 35.20Euro.

A third way is to take the SENA bus from Siena to the Tiburtina train station in Rome. Take the metro 4 stops to Rome Termini where you pick up the high-speed to Naples. A bit less money but you are still looking at 7.0hrs.

Once in Naples Centrale, you go a level and next door to the private Circumvesuviana train station and take the 1hr. train to Sorrento.

If you travel by bus to Rome Tiburtina, consider using either the Marozzi or Curreri bus services starting there. They go directly to Sorrento, the journey takes about 3.5 hours.

PS Marozzi appear to have a bus, leaving Rome at 7.00 am, via Sorrento to Amalfi

http://www.curreriviaggi.it/

http://www.marozzivt.it/web.aspx