In Mainz operates the MVG (Mainzer Mobilität) a system of reliable local busses and trams. Ticktes are available at ticketmachines at the plattform and the conducter sells them.
A single ticket costs 2,80€. But if your route ranges less than 3 stations the MVG offers a single ticket for short distances “Kurzstreckenticket” for 1,75€ (e. g. “Mainz Hauptbahnhof” – “Universität Mainz”).
Website of the MVG (German only).