Police said they suspected the driver lost control at 8:00 am (0200 GMT) and hit the railing of a recently built major expressway, sending the bus tumbling 30 feet (nine metres) into the ditch.
"The death toll has risen to 19. At least 12 people were critically injured. They have been sent to Dhaka Medical College Hospital in the capital," local police chief Masud Alam told AFP after the crash in the southern district of Shibchar.
Road accidents are frequent in Bangladesh due to old and badly maintained vehicles and roads, as well as poorly trained drivers.
According to the Bangladeshi passengers' welfare association, a record 9,951 people were killed in road accidents in Bangladesh last year.
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