He married Margaret Amy Beatrice Owen, from England, on 16 June 1897, with whom he had one son, William Bury.

Bury's first attempt at public office was running for the Legislative Assembly of Alberta in the 1921 provincial election as a Conservative in Edmonton.

However, Parliament was dissolved amid the King-Byng Affair the following year, and Bury was narrowly defeated in the ensuing election by Liberal (and incumbent mayor of Edmonton) Kenny Blatchford.

Bury defeated Blatchford by a substantial margin in the 1930 election as R. B. Bennett's Conservative government swept to power.

"erected a flaming cross on the hill above Riverdale flats to celebrate the victory of Edmonton East candidate Ambrose Bury.

He was appointed as a district court judge that year, and served in that capacity until he reached the retirement age of 75 in 1944.