During the summer, there is also a DIRECT Marozzi bus from Rome Tiburtina to POSITANO, but it departs Rome only at 7:00 a.m., making it feasible only for people who have overnighted in Rome.
There are also afternoon buses from Rome Tiburtina to SORRENTO by both Marozzi and Curreri. In Sorrento, you can connect to the regular SITA bus to Positano.
The previous postings reflect the fact that there are MANY different ways to travel between Rome and Positano, ALL of which require transportation changes/connections (some fewer, others more).
www.marozzivt.it
www.curreriviaggi.it
HINT #1: Staying on the Amalfi Coast for at least three days: consider purchasing the 3-day UNICO COSTIERA ticket for 18 Euros. You get unlimited rides on all SITA buses between Salerno and Sorrento, including Ravello. (NOT valid on ferry boats or hydrofoils).
HINT#2: Staying at least three day and also going to Paestum or Pompei or Naples? Consider buying instead the UNICO CAMPANIA 3T Tourist ticket for 20 Euros. It's valid for the entire Campania region on all SITA buses, Trenitalia regionale trains, Circumvesuviana trains, Naples city buses and funiculars, Mt. Vesuvius buses, Sorrento city buses, and more. (It also covers everything which is covered by the UNICO COSTIERA tickets).
Remember:
Amalfi Coast only: UNICO COSTIERA (45-min, 90-min, 1-day or 3-day tickets)
Amalfi Coast and surrounding areas for 3+ days: UNICO CAMPANIA 3T Tourist Ticket.
UNICO CAMPANIA also sells one-way and 1-day tickets