Below there are several ways how to reach Civitavecchia from Rome.
Here is the timetable from-to Civitavecchia. This is valid from 11.05.2016 till 08.07 2016.
Cotral: Civitavecchia – Roma
From Civitavecchia buses leave from bus terminal Dep.Cotral/Braccianese, from bus stops Ospedale S.Paolo and Porta Tarquinia. During work days buses to Rome from Dep.Cotral/Braccianese levae evry 30 min, during holidays every hour. From Porta Tarquinia to Rome buses leave once a day at 14:10, that passes after the bus stop Ospedale S.Paolo.Note: those who arrive in Largo della Pace the most closest bus stop is Porta Tarquinia.
In Rome the bus station is Cornelia (near the same named metro station of line A).
One way ticket costs 3.90 EURO from Porta Tarquinia and 4,50 EURO from Dep.Cotral/Braccianese.
There is also a possibility to take a train. From the train station of Civitavecchia/ital. Stazione Ferroviaria di Civitavecchia leave reagional, inter city and freccia bianca trains. They arrive at Roma Termini. The average journey time is an hour and 15 min.
Check this for more information about Civitavecchia connections.
Check this for more information about COTRAL