To reach the town of Tivoli, there is a direct line from Rome, departing from the metro station, line B / blue, Ponte Mammolo. The service is provided by the company Cotral. The town is famous for its famous Hadrian’s Villa/ital. Villa Adriana that is a villa of Roman Emperor Hadrian which is now a hige archeological complex, the castle of Rocca Pius II, gorgeous Villa d’Este and Villa Gregoriana.
The buses run from the metro station Ponte Mammolo in direction Tivoli every 10 minutes and the bus trip lasts approximately 50 minutes. How to get to metro line B you can check here: Rome metro linea B
Tickets can be purchased from authorized dealers Cotral, even within the metro station Ponte Mammolo.
The timetable in a pdf fromat: Cotral: to and from Tivoli
For further information please check the schedule of the company Cotral