For traveling between Frankfurt Airport and Mainz it is highly recommended to take the train. The Airport has two separate train stations, one for regional train traffic and one for the intercity train traffic.
The most convenient connection is the train S8, which departs every 30 minutes from the regional train station of the airport.
For information on specific train connections, we advise you check Deutsche Bahn for an overview.
A Single ticket between Mainz and Frankfurt Airport costs 5,80 €. Additional information is provided by the RMV