Preferred route from Rome to Amalfi (no car)

I would take the train from Roma all the way to Salerno.
Then from Salerno station, you can take a bus or a boat to Amalfi. The harbor is just a few short blocks from the train station.
www.trenitalia.com
for train timetable and prices.

But are you asking how to get to Furore? There is no ferry or train service there, and it's a handful of miles from Amalfi so you'll probably need to take a bus or taxi from there. Where are you staying, and can they provide a suggested transport method to/from that accommodation?

If you want Furore you need another bus from Amalfi (the Amalfi-Sorrento bus). There is also a taxi stand in the piazza in front of the harbor. Shouldn’t cost too much, it’s only 10 km or less. Maybe 25€? But the bus is cheaper.

One bus schedule to/from Amalfi:

http://www.sitasudtrasporti.it/archivio/Download/corse/sitasud/Campania/Salerno/18167f74-2866-412c-b2c9-506f3e72e0f8_5080_INV.pdf/0

Not sure there's an alternate but I'm looking, and your accommodation should be able to help. :O)

Thanks for the responses and the link to buses. I will spend some time interpreting it. Also I appreciate the advise to contact my host for navigating the last bit of travel to Furore. It appears that the more direct route with fewer transfers is Salerno as opposed to Sorrento. Correct?
Thanks

If you go to Salerno, it’s one high speed train from Rome to Salerno. Then one bus to Amalfi. Then from Amalfi to Furore it’s another short bus ride (or taxi ride).
If you go Via Sorrento, it’s one high speed train to Naples. Then a commuter train from Naples to Sorrento. Lastly one bus from Sorrento to Furore.
So, no matter what, for Furore it’s 3 modes of transport.
Train+train+bus (Via Napoli and Sorrento)
or
Train+bus+bus (Via Salerno and Amalfi)
I prefer the Salerno option because I don’t like the Circumvesuviana train from Napoli to Sorrento.
Also from Salerno you can take a boat to Amalfi, which would be the best).

Agreeing with Roberto that the route he suggested is best.

Having done a little more digging around, because Furore is lightly strung along a series of switchbacks heading up the steep side of the of the coast, depending on where your accommodation is you'll probably need to change buses which serve the more upper reaches to those which serve the lower to get to certain destinations by land.

This is the schedule for the Sorrento> Amalfi bus, which is very busy during high season and which you will probably be connecting with if you, say, want to go to Praiano.

http://www.sitasudtrasporti.it/archivio/Download/corse/sitasud/Campania/Salerno/c4087537-7425-4efa-96f6-3737a1fdae8e_507_INV2.pdf/0

Scott--

Roberto's plan is solid. Freccia train from Roma Termini stops in Naples but goes on to Salerno--1 hr, 54 min in total--a no-brainer. From Salerno Centrale station, hop on a bus to Amalfi. I believe the bus originates there, so you should get seats. 1 hour. Maybe 4 Euro? Good views from driver's side, maybe not for your wife, though!

From Amalfi to Furore, I'm sure Kathy can set you up with a burro or something similar... :)

1 burro coming up! Giddiyup, ya'll. 🐎

Editing to add, Jay brings up a very good point? If your wife has a queasy stomach on water, she should bring anti-nausea medication along for the Amalfi Coast buses as well. My own tum couldn't handle a road trip just from Sorrento to the Naples Airport.

Thank you all. I will follow your kind advice.
Scott

Bus timetable Amalfi-Furore and beyond.

http://www.positano.com/en/bus-schedule?bus_route=amalfi_agerola