Getting from sorrento to Rome

Circumvesuviana or private driver to Napoli Centrale
Then fast train to Rome

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From a Search here. It's a weekly topic. There is no quick and easy way to travel in such a congested area that lacks adequate infrastructure.

Have a great trip!

There is also a bus which will get you to the train station. Going Sorrento to Naples central station that way might be easier, though I have usually opted for the train.

I have thought this through and we decided to hire a private driver to pick us up at our Sorrento hotel (Il Nido) on the day we depart Sorrento, a Sunday morning 8am in mid-October to take us to the Naples main train station. Sometime soon I will buy fast train tickets from Naples to Rome and we will hopefully arrive at our hotel in Rome where our Rick Steves Heart of Italy tour begins at 3pm that afternoon from the hotel.

Will I be able to buy fast train tickets at the Naples central train station on the Sunday morning we get driven from Sorrento to Naples?

Probably
But if you already know date and approx time you can purchase in advance on Trenitalia website or on the easy to use ap

ItaloTreno also runs fast trains Naples to Rome, also has an app

At least familiarize yourself with the schedules so you have an idea of which train you’ll likely be taking

The trip takes about 1 hr 15 min, then you’ll need to get to your hotel from Termini so I’d want to be on a train leaving Naples by 11ish
There are several trains between 10-12

The stations you want are
Napoli Centrale
Roma Termini

I would just grab a cab from Termini to hotel-from official taxi line-shouldn’t be more than 10-12 euros
Unless hotel is within walking distance

The train to Naples from Sorrento is cheap and convenient, from their there are plenty of trains all day to Rome.