The accident occurred on Wednesday when the bus lost control approaching a ferry at Daulatdia in Rajbari district, about 100 kilometres from Dhaka. The bus overturned and sank nearly nine metres into the river, according to police and the Fire Service and Civil Defence.
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Rescuers recovered 22 bodies from inside the submerged bus, including six men, 11 women and five children, Fire Service official Talha Bin Zasim said.
Twenty-four people have been confirmed dead so far, including two women who died after being rescued, he said.
Four fire service units and 10 divers were leading the search and rescue efforts, supported by the army, police, coast guard and local authorities.
Officials fear more passengers may still be missing. Hundreds of people die each year in road and ferry accidents in Bangladesh.