Meridian, the private company that runs regional trains between Munich and Salzburg has a day ticket (Tageskarte) for their track network for 2€ less than the Bayern-Ticket. It's called Guten-Tag-Ticket (page in German) and sells for 21€ for the first person, 4€ for each additional person up to 5 total (also parents or grandparents with all of their children/grandchildren under 15). Same conditions as the Bayern-Ticket, after 9 AM workdays. The track network for Meridian is here. The ticket is also valid on the track network of the Bayerischeoberlandbahn (BOB) south of Munich (Bad Tölz, Tegernsee, Schliersee).
You can purchase the Guten-Tag-Ticket from Meridian ticket automats in all stations, from the Meridian customer service counter by track 30 in the Munich Hbf, at the DB Reisezentrum in Ostbahnhof, and from the Meridian WEB-SHOP. If you can't find a counter or automat, you can also buy tickets on the train without a surcharge.
Note: this is a much more limited area than the Bayern-Ticket and buses are not included. Also, conveyances of the MVV (Munich metro) are not included, so it would not be cost effective if you needed to get from somewhere in Munich to the Hbf or to Ostbhf by public transportion (the link between the Hbf and Ost is the rail line, not the S-Bahn.