After graduating from high school in 1940 he studied violin with Walther Davisson at the University of Music and Theatre Leipzig.
In 1943 he was appointed to the Reichs-Bruckner-Orchester in Linz and played under conductors like Karl Böhm, Wilhelm Furtwängler, Carl Schuricht, Herbert von Karajan, Oswald Kabasta and Joseph Keilberth.
In 1949 Bosse became professor at the Hochschule für Musik Franz Liszt, Weimar and in 1951 first concertmaster of the MDR Leipzig Radio Symphony Orchestra under Hermann Abendroth.
From 1955 to 1987 Bosse was concertmaster of the Gewandhaus Orchestra under the conductors Franz Konwitschny, Václav Neumann and Kurt Masur.
In 2000, he became music director of the Kobe City Chamber Orchestra and two years later advisor to the New Japan Philharmonic.