4 of us are taking private transport from Rome to Positano, and would like a less expensive way to travel back to our hotel in Rome. We will have luggage and would like to minimize the number of transfers, while still saving some euros. Would appreciate any suggestions you might have!

I believe there is a bus from Sorrento to Rome but it may run only once or twice a day and you would need to check timing versus getting there from Positano - by taxi I presume for 4 with substantial luggage

We did this the other way around, but I think it's a great option: ferry to Salerno, then direct train to Rome. I't less than 5 minutes walk from the ferry terminal to the train station. Out train made only 1 stop in Naples.

We just did this in April. travelrelax.com picked us up at our hotel and brought us to Napoli Centrale train station. Cost 90 euros for the car. Friendly, reliable and professional. The owner's father was our driver. High speed train from Naples to Roma Termini took 1hr 10min. Booked tickets in advance through trenitalia.com. Booked travelrelax in advance through their web site. This is the way to do it.

^
I agree with letsgeaux - this is the way to do it, although I haven't done it yet!

In September my husband and I will be travelling from Sorrento (our hotel in the hills!) to Napoli Centrale with www.guemartravel.com for 80 euros, then catching high speed train Naples to Roma Termini.
Communication with them has been fast and fabulous!

The ferry to Salerno and then a direct train to Rome plus a taxi to your hotel would be by far the most economical system. The private driver to Naples would be quicker, and the cost, shared among four people, shouldn't be excessive.

Both systems will have the same number of transfers.

The Marozzi bus to Rome picks up in Positano in summer so it would depend on when you are traveling. Cost is 21€. The times may not work for you as it's 4pm, but there are no transfers and your luggage is stored under the bus. At other times of the year, you can catch the bus in Sorrento (a few euro cheaper than from Positano). Sorrento has a 6am departure so you would need a driver Positano/Sorrento very early or take the late bus.

Thanks to all for the many suggestions for travel. Letsgeaux, I was not able to open a site for travelrelax in English. Is there a trick for this.
Also, like the idea of ferry to Salerno, then train to Rome. Is it advisable to wait until we get there and then figure out how to get to ferry terminal or do this in advance?? Taxi possible?

Sorry for the bad link. It is transferelax.com. Highly recommended.