Bischof was born in Zürich, Switzerland. When he was six years old, the family moved to Waldshut, Germany, where he subsequently went to school. In 1932, having abandoned studies to become a teacher, he enrolled at the Kunstgewerbeschule in Zürich, where he graduated cum laude in 1936. From 1939 on, he worked as an independent photographer for various magazines, in particular the renowned magazine du based in Zürich. He travelled extensively from 1945 to 1949 through nearly all European countries from France to Romania and from Norway to Greece. His works on the devastation in post-war Europe established him as one of the foremost photojournalists of his time. In 1949, he joined Magnum Photos, which at the time was composed of just five other photographers: Robert Capa, Henri Cartier-Bresson, George Rodger, David Seymour, and Ernst Haas. The focus of much of his post-war photography was showing the poverty and despair around him in Europe, tempered with his desire to travel the world, conveying the beauty of nature and humanity.
In 1951, he went to India, working for Life magazine, and then to Japan and Korea. For the magazine Paris Match he worked as a war reporter in Vietnam. In 1954, he travelled through Mexico and Panama, before flying to Peru, where he embarked on a trip through the Andes to the Amazonas on 14 May. On 16 May his car fell off a cliff on a mountain road in the Andes, and all three passengers were killed. Fifty years later his son Marco gathered 70 previously unpublished photographs of his father's in Questions To My Father.