Ideally, for this hike, if possible one should use a car to drive to Linderhof from/to where the hike starts/ends.

Alternately, one needs to take regional trains from Munich to Oberammergau (via Murnau), from where the bus 9622 can be taken to Linderhof. The schedule of the bus can be seen here: https://www.lra-gap.de/media/files/lra_kfz-verkehr_oepnv/Busplan_Linie_9622.pdf

In case, the time is an issue, during the descent, one could deviate from the route a bit, and take the bus from kenzenhuette to Halblech. This shortens the route length to 12.5 km, however, the bus from Kenzenhuette is not included bayern ticket, and one needs to pay extra (~5 Euro). From Halblech one could take bus 73 to Fuessen hbf, from where there are regional trains to Munich until pretty late.