Bermuda were struggling at 17-3 in 7.4 overs, with opener Oliver Pitcher batting on eight and skipper Irvine Romaine on one. Stephen Outerbridge, Delyone Borden and David Hemp were the batsmen dismissed.
Fast bowler Mashrafe Mortaza took two wickets and Syed Rasel one.
Bangladesh captain Habibul Bashar elected to field in overcast conditions after winning the toss in a match his side needed to win to qualify for the second round.
Bangladesh have beaten India in their first match in the four-team group, while Bermuda have lost both of their games against India and Sri Lanka.
Sri Lanka were the first team to qualify for the Super Eights with an all-win record.
India have finished their group campaign with one win and two defeats. Their lone win came against Bermuda, the weakest side in the group.
The top two sides will make it to the next round.
India can still qualify for the second round if Bermuda beat Bangladesh.
Bangladesh retained the side that lost to Sri Lanka by 198 runs in the previous match.