I've ridden on many RVO buses in that area, but not on RVO 9556. All have been covered by the Bayern-Ticket.
The RVO (Regionalverkehr Oberbayern) is a subsidiary of Deutsche Bahn.
From the Beförderungsbedienung (conditions of service) of the RVO,
6.5.1 Bayern-Tickets
In den Bussen der RVO GmbH werden folgende Tickets anerkannt
Bayern-Ticket
Bayern-Ticket Nacht
Bayern-Böhmen Ticket
Auf bestimmten Strecken ist eine Maut zu bezahlen. Bei ausländischen Strecken gilt das Bayern-Ticket
bis zur letzten deutschen Haltestelle (Ausnahme: Salzburg Hbf.).
Bayern-Tickets werden auch in den Bussen der RVO GmbH verkauft, hier gilt der Preis für den Automatenverkauf.
Bayern-Böhmen-Tickets werden in den Bussen analog zu den Bayern-Tickets anerkannt, jedoch nicht verkauft.
Das Bayern-Ticket und das Bayern-Böhmen-Ticket werden auf folgenden Strecken nicht anerkannt:
Linie 847 ALM-ERLEBNIS-BUS
Linie 849 Kehlstein Busabfahrt – Kehlstein Parkplatz
(The translation is left to the reader as an exercise.)
But, basically, the first three items are accepted on the RVO, including a Bayern-Ticket. The two lines listed at the end are not included in the Bayern-Ticket, including the special buses (849) that go up the closed road to the Eagles Nest.
The Bayern-Ticket is not accepted for portions of lines that go outside Germany (see Liniennetz), particularly on the part of the Watzmann Express, RVO 840, from Salzburg to Marktschellenberg. The out-of-Germany portion of the line between Füssen and Reutte, Austria, also does not accept the Bayern-Ticket.
You could also use the Bayern-Ticket on RVO 9550 to Walbergbahn, which parallels 9556, but you might have to tell the driver you weren't going on to the portion of that line that goes into Austria.
By the way, Google maps shows the distance between Tegernsee Bhf and the Wallbergbahn to be between 6 and 7 km, depending on the route. The RVO website gives the adult fare as 2,90€ for 4-6 km and 3,40€ for 7-10 km, but what's 6-7 km?