Born to a Jewish family[1] in Hartford, Connecticut, Bischoff graduated from Boston University, then headed for Hollywood, where he began his career in 1922 by producing comedy shorts including Stan Laurel's Mixed Nuts (1922).

He drew the attention of Columbia Pictures head Harry Cohn, who hired him to supervise the studio's feature film productions.

In 1932, he moved to Warner Bros. and when Hal B. Wallis became production chief after Darryl F. Zanuck left in 1933, Bischoff and Henry Blanke were the main producers at the studio.

He was also the President of Moroccan Pictures Inc. in 1948, producing the George Raft film Outpost in Morocco (1948).

In 1950 he became production chief at RKO replacing Sid Rogell but did not stay long.