The accident occurred when the driver lost control of the vehicle near Jessore district.
The bus was going to Benapole in Jessore from Dhaka.
"The bus hit a tree at Godkhali on Jessore-Benapole road as the driver lost control over the steering around 6:30 am", said Mosharraf Hossain, officer-in-charge of Jhikorgachha Police Station.
Six passengers died on the spot while four succumbed to their injuries at Jhikorgachha Upazila Health Complex and Jessore Medical College and Hospital, Assistant Superintendent of Police Sharmin was quoted as saying by the Daily Star.
Bangladesh has one of the highest fatality rates for road accidents in the world mainly due to dilapidated highways, poorly maintained vehicles, violation of traffic rules and lack of monitoring of the traffic department.