Bruck studied at the University of Toronto, where he received his doctorate in 1940 under the supervision of Richard Brauer.

[1] He spent most his career as a professor at University of Wisconsin–Madison, advising at least 31 doctoral students.

In 1956, he was awarded the Chauvenet Prize for his article Recent Advances in the Foundations of Euclidean Plane Geometry.

In 1965 a Groups and Geometry conference was held at the University of Wisconsin in honor of Bruck's retirement.

Dick Bruck and his wife Helen were supporters of the fine arts.