The only Bus Transport I found to and from Burgen was a Bus that travelled between Koblenz and Burgen.
The nearest Train Station was about seven miles away at Lof, on the other side of the Mosel River. There were a couple of regular services from this station, the one I used ran between Koblenz and Trier.
To get to the station I used a Taxi service based in Lof, they charged me Fourteen Euros each way...Regins's Clubreisen Taxi. Tel. 02605/4700