From Rome to Amalfi Coast

I don't believe there is such a boat.
You can take a train to Naples and then get one another train at the same station to Sorrento though.
Sorrento has a train station.

There are also buses from Rome to Sorrento (stops in between a few times though so the train is faster, some still prefer the bus since no change is required)

Lastly you can train to Salerno and see the coast from that side. Depending on where you are staying on the coast that may be better than Sorrento.

There is a ferry but not worth the effort. Have to take a cab or tram from the Naples to the port. Are asking about a day trip - a little far for a day trip ? or an overnight in Sorrento?

With 4 nights at the end of your trip, you could spend 3 nights in Sorrento and return to Rome for your last night. It's easy to explore Pompei, Amalfi Coast, Capri, Naples and other nearby destinations using Sorrento as your base. Travel time between Rome and Sorrento is 4-5 hours each way, depending on connections.

Do you know the name of the bus company from Rome to Sorrento? I Would like To explore this Option instead of a train.

Maria, it would be best if you started a new thread with your question so people so people don't get confused with the OP's thread.

I'm curious why you want to to "explore this option instead of a train"? Some buses can be OK but others tend to have far fewer daily runs than the trains, and are more prone to traffic complications.

We have taken the Circumvesuviana commuter train and while it's a battered, un-lovely, un-airconditioned thing, it's how the locals get around. Keep your valuables under wraps - as you should almost anywhere AT ALL in Italy - and you'll be fine. It's easier from Centrale than transferring to the docks for a ferry.

Try this one. All dates may not be available yet so keep checking.

https://shop.flixbus.com/search?rideDate=16.04.2018&adult=1&children=0&bike_slot=0&route=Rome-Sorrento&departureCity=2075&departureStation=&arrivalCity=13128&arrivalStation=&_locale=en

check the Rome2Rio website. Offers you all travel options.

check the Rome2Rio website. Offers you all travel options.

Rome to Rio isn't always the best resource depending on what form of transport one is taking.

My husband and I spent a few days in Rome and then took a Frecciarossa to Salerno as a base camp while we explored the Amalfi coast. We highly recommend Salerno as it has access to trains, to buses and to ferries. We used the ferries extensively to get to the towns on the Amalfi Coast. We wanted to avoid the Circumvesuviana at all costs! Unfortunately we had to use this local train to get to Sorrento as the ferry was not in operation at that time. What was described in another post is absolutely true. It is rickety and full of panhandlers. It stops many times, and during our trip, some loud disruptive teen boys hopped on and off as there was no conductor to check tickets or monitor behavior. Rick has warned about pick pockets on this train as well. That being said, if you take the ferry to Sorrento,, be sure to eat lunch at Delfinos on Marina Grande! The Amalfi is gorgeous! Our favorite spot was Ravello, above the town of Amalfi. The view is breathtaking! You could take the fast train back to Rome if you fly out from there, or take a train to Naples to return home. Enjoy every minute! We would go back in a heartbeat.

Barb,
My wife and I also exploring getting AirBnB in Sorrento/Salermo area for a few days to check out that area. Will also be taking train down from Rome and then departing for Italy's Aegean coast and north in a rental car. Was there lots of opportunity for arranging bus,ferry etc. to explore Amalfi area after you got to Salermo?
Anyone rented a car in Amalfi area with eventual drop off in Milan?

There are ferries that regularly go up the coast and stop in Amalfi and Positano. I think you can also ferry up to Sorrento, but when we were there, that leg was closed due to old WW2 munitions found there. I am not sure about the ability to rent a car in Salerno, but you could google it.