Born in Lübeck, he graduated with honours from the Cologne University of Music (Hochschule für Musik und Tanz) and the Robert Schumann University of Music and Media in Düsseldorf, where he studied piano with Günter Ludwig and David Levine as well as conducting with Volker Wangenheim. He began his career as a concert pianist. After attending masterclasses with Leonard Bernstein, Sergiu Celibidache, and John Eliot Gardiner, in 1988 he became the chief conductor of the Tübingen Sinfonietta, with which he worked until 1996, also collaborating with Brussels’ Théâtre de la Monnaie, as well as theatres in Basel and Lübeck. In 1997–2007 he was the artistic director of the Zeitgenössische Oper in Berlin, where he premiered works by Henze, Kagel, Battistelli, Feldman, Reimann, Hölszky, Martin, Sciarrino, Maxwell Davies, Rihm, and Holliger. At the 2002 Munich Biennale he led the German Youth Orchestra in the world premiere of André Werner’s opera Marlowe: Der Jude von Malta. Subsequent invitations brought him to Munich, Vienna (Klangforum Wien), and Dijon (Why Note Festival), the ensembles of the Collegium Novum and Neue Musik Berlin, as well as festivals such as Ultraschall Berlin and the Venice Biennale. With the European Workshop for Contemporary Music, he has appeared many times at the Warsaw Autumn Festival. 

As an orchestral conductor he has worked mainly outside Germany. He has cooperated with the RAI symphony orchestras in Rome and Turin, Orchestre de Chambre de Lausanne, Orchestre de la Suisse Romande in Geneva, Orchestre Radio-Symphonique du Luxembourg, as well as the orchestra and choir of the Teatro Comunale di Bologna. He has also appeared as a guest conductor with the Österreichisches Ensemble für Neue Musik at the Salzburg Festival, and London’s Philharmonia Orchestra. He regularly conducts ensembles and orchestras in South Korea (Tongyeong International Music Festival, Seoul Philharmonic, and Seongnam Philharmonic) and Japan (Next Mushroom Promotion Ensemble, Takefu Festival). Since 2003 he has been the Artistic Director of the European Workshop for Contemporary Music. 

Bohn is a professor of conducting at the Robert Schumann University of Music and Media in Düsseldorf. He collaborates with such composers as Beat Furrer, Toshio Hosokawa, Isabel Mundry, Wolfgang Rihm, and José María Sánchez-Verdú. 

In 2017 he received the Decoration of Honour for Services to the City of Warsaw.