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.
The Empress was curious about the performances of "the Silver Turk" at the Vienna Exposition. In a letter sent with Ernst Bratfisch, she invited Alfred Stahlbaum to attend the Hofburg Palace with the Silver Turk. However, the was made impossible when Gramm managed to catch up with Stahlbaum as he was already turning into Hofburg and rob him of the opportunity to show off the Silver Turk.
Knowing about Stahlbaum's obsession with the Empress, Puppet Johan Drossel employed a puppet of the Empress to try to persuade Stahlbaum to join forces 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.