There is a Lufthansa bus from Munich main station to MUC:
https://www.airportbus-muenchen.de/ (it's just called Lufthansa Express Bus, but it doesn't matter which airline you fly from MUC).
Single ride is 10.50, return is 17 Euro, if booked online.
I personally would do ICE Mannheim->Munich and then the Lufthansa Bus, if wouldn't want to use the S-Bahn.