Her title during the events was Elisabeth of Austria. Neither "of Austria" nor "of Bavaria" is mentioned in the play.
Talk about it here.
Elisabeth of Austria, commonly referred to by her pet name Sisi, was the wife of Emperor Franz Joseph I of Austria and, thus, the Empress of Austria, when the Eighth Doctor visited Vienna with Mary Shelley in September 1873.
Alfred Stahlbaum was hoping that the performances of the Silver Turk at the Vienna Exposition would be noted by the empress or her royal husband. Knowing about this obsession, Puppet Johan Drossel employed a puppet of the Empress to try to persuade Stahlbaum to work with him again. (AUDIO: The Silver Turk)
Behind the scenes
Elisabeth was Empress of Austria, Queen of Hungary and Queen consort of Croatia and Bohemia. She was quite loved by her subjects and her beauty has become legendary. This has inspired multiple movies in which she was portrayed by such stars as Romy Schneider and Ava Gardner. At the same time, her nickname has been often misspelled "Sissi". Part of the Hofburg Palace is a dedicated Sisi Museum.