There are several options for travel from the Amalfi Coast to the Napoli Centrale train station. It all depends on which town you are staying in.
If your lodging is between Amalfi town and Salerno, take the ferry, weather permitting, to Salerno. Walk across the street and take the train to Napoli Centrale ( you can ticket yourselves through to Camucia-Cortona, but will still have to change trains. )
Other option besides the bus is to ferry to Sorrento. From here 2 other choices... Ferry to Naples, then Alibus to train station or Circumvesuvian to Naples. Napoli Centrale is upstairs. Ticket would then be Napoli Centrale-Camucia-Cortona with one change in Rome. Train time about 4 hours.
Ferry & bus schedules here.
http://www.positano.com
For train use Trenitalia.com
Make sure you can rent a car in
Cortona. Use Auto Europe or Kimwel. Both parts of the same company, but offen different pricing.