Meanwhile, Warner, hit his 16th ODI hundred when rain stopped play, in the process equaling India skipper Virat Kohli. Warner became only the second batsman to complete 16 ODI tons in 110 innings.
Hashim Amla, who scored his 16th ODI century in 94 innings, holds the record for fewest innings to this feat.
Warner's first century came against Pakistan in Taunton. In Australia's first game, Warner scored an unbeaten 89 against Afghanistan.
Warner added 121 runs with his skipper Aaron Finch (53) in a risk-free opening partnership and then raised a 192-run stand with Usman Khawaja (89).
The win took Australia to top of the table with 10 points from six games while Bangladesh remained at number five with five points and now need to win their remaining three games.
Earlier, medium pacer Soumya Sarkar (3/58) took three wickets while Mutsafizur Rehman (1/69) accounted for one Australian batsman.