From a gymnast colleague of mine:
http://www.turngau-muenchen-geraetturnen.de/Proper gymnastics with apparatus etc. is "gerätturnen" - just "gymnastics" or "turnen" seems to mean things like stetching classes and aerobics.
There is a list of clubs on the links page. He couldn't recommend any specific one, but said that if you really had problems finding something, he could try asking around.
My colleague also said that there are plenty of competitions for adults, including Bavarian championships.