Yes, but the final destination is Amalfi. The bus leaves from Rome Tiburtina Station on the Via Ostiense (not Stazione Termini) and is run by the Marozzi company. The trip lasts about five hours (longer if you continue to Amalfi). It leaves at 7 a.m. on weekdays and 3 p.m. on Sunday and holidays. In summer, there are two departures — morning and evening — on Friday, Saturday, and Sunday. You can get one-way or roundtrip tickets at the station. Here’s the timetable.
For those of you who have early-arriving flights to Fiumicino, the morning bus is out of the question unless you clear customs by 6 a.m. and few flights, even with tailwinds, ever arrive that early from North America.