However, Dutch hopes were dashed when Sybrand Engelbrecht's entertaining innings of 33 off 22 balls came to an end in the 15th over.
Bas de Leede (0), captain Scott Edwards (25) and Logan van Beek (2) all departed in the space of six runs as they tried to accelerate.
Leg-spinner Rishad Hossain was the best bowler for Bangladesh, taking three wickets for 33 runs in four overs.
In their final group match, Bangladesh will face Nepal, who still have hopes of making it to the Super Eights if they beat the Tigers and Sri Lanka.
So far, four teams have secured their place in the Super Eights – South Africa, India, West Indies and Australia.