Born in Nuremberg, Bittner attended the Realgymnasium and the Hochschule für Musik Nürnberg and completed private music studies with August Scharrer and Richard Lert.
He began his career as 2nd Kapellmeister at the Reussisches Theater Gera [de] (1923-1929), which was one of the most "advanced" theatres in the German Reich in the 1920s due to its programme and attracted many prominent artists.
In the 1932/33 season he was subsequently first Kapellmeister at the Graz Opera, where he also joined the National Socialist German Workers' Party (member number 1,517,656).
He also brought out a number of important premieres, including the Irische Legende by Werner Egk, Die Schule der Frauen by Liebermann and Strobel, Dimitrij by Dvořák/Marie Červinková-Riegrová and Die Heimkehr (staged premiere 1955) by Marcel Mihalovici for the first performance.
In September 1970, on the occasion of his 70th birthday, he conducted a performance of Mozart's The Magic Flute; this was also his last appearance on the podium of the Hamburg State Opera Orchestra.