Alternatively, you can try AirBNB. There is a chance to get a price tag of around 36,3 - 48,4 USD = 30 - 40. EUR View AirBNB housing in Bavaria:
With minimal knowledge of German, you can look for rental housing in local villages. The site of the district center almost always looks like www.name_city.de Look for the Tourismus section or something like that, then the Übernachtung section. There are guesthouses, privatzimmer and so on. Example: starnberg.de. You need to call and find out if there is a spare room.