München to Thierhaupten

Eurolines sells tickets from Munich to Augsburg for 5 Eur (apparently only one bus leaving at 17:30). These are far distance coaches, so check with the company for possible delays before you book.

From Augsburg to Thierhaupten with the Augsburger Verkehrsverbund costs 9 Eur. For connections, see also lines 410 and 410/413 on the web page of Thierhaupten.

Possible itinerary for April 4, 2019, cheap but not easy:

Eurolines
17:30 Munich, central coach station
18:30 Augsburg, Biberbachstrasse 9

walk, 6 min

(Unfortunately, you've just missed the last bus 410 from Oberhausen, Nord P+R to Meitingen/Thierhaupten at 18:24.)

Tram/Straßenbahn 4 > Augsburg, Hbf 
19:37 Oberhausen, Nord P+R
19:45 Augsburg, Wertachbrücke (*)

Tram/Straßenbahn 2  >  Augsburg, West P+R   
19:48 Augsburg, Wertachbrücke
19:50 Oberhausen Bf/Helmut-Haller-Platz 

Regional train/Regionalbahn R4 > Donauwörth, Bahnhof
19:57 Augsburg Oberhausen Bf/Helmut-Haller-Platz    
20:13 Meitingen, Bahnhof

Bus/Regionalbus 410/413
20:20 Meitingen, Bahnhof
20:33 Thierhaupten, Marktplatz

(*) This is the suggested route by the Augsburger Verkehrsverbund. If you are early, you could also continue to Augsburg Hbf instead and take the R4 train from there.

You can get from Munich to Thierhaupten by a combination of train and bus. Visit bahn.de for detailed information. Selecting "München Hbf" as the starting point and "Marktplatz, Thierhaupten" as the destination gives prices between €20 and €30, depending on the trains involved.

If you want to hitch a ride in a car there is a ride sharing site called Mitfahrzentrale, without a guarantee that you find something which matches your needs.