Bigg first ran for a seat in the House of Commons of Canada in the 1958 federal election.
Bigg ran for re-election in the 1962 federal election, once again he defeated three other candidates in a closely contested race to win a second term in office.
Parliament was dissolved a year later after the minority government fell forcing the 1963 federal election.
Bigg ran for a third term in office and was returned in a landslide defeating two former Alberta MLAs Richard Hall and Peter Chaba and another candidate.
He won the largest plurality of his career and was re-elected to his fifth and final term in office.