Brian Bancroft obtained his Bachelor of Architecture from the University of Manitoba in 1964. In his final year, he submitted a design to the national Pilkington Travelling Scholarship competition. Bancroft was awarded the second prize for the design of a fishing village. The same year he graduated, Bancroft joined the Winnipeg-based architectural firm Smith Carter.
In his early years with the firm, Bancroft was involved in the design of projects including the Liquor Control Commission Head Office and Warehouse and the Pan Am Pool. By July 1968, Bancroft was appointed as an associate. Just two years later, Bancroft was appointed as Director of Design for the firm.