During Bevington's term at the head of council, Fort Smith recognized the Chipewyan and Cree languages, making the town officially quadrilingual.

In the 2000 federal election he ran as the NDP candidate for Western Arctic, but lost by 18% to incumbent Ethel Blondin-Andrew.

On October 19, 2015, Bevington was defeated for re-election by Liberal candidate Michael McLeod.

[1] Bevington fought for years to have the name of the riding changed from Western Arctic to Northwest Territories.

[2] Since 2008, Bevington has tabled three private member's bills titled "An Act to change the name of the electoral district of Western Arctic", all dying on the order paper.