Don't know about shuttle buses.
If you like it cheap select as means of transport "only local transport". And give
Than you can buy at Frankfurt airport from ticket machines:
1. normal ticket to Mainz EUR 3,70
2. Rhineland-Palatinate Ticket EUR 19,00
Rhineland-Palatinate Ticket covers the regional trains and buses in the state Rhineland-Palatinate.
You could also travel by train to Landstuhl or Altenglan and taxi from there.