Passengers jumped from the windows - some engulfed in flames - as the bus veered off the road and crashed into an electricity pole in the Bangladeshi capital Dhaka, police said.
"I carried four passengers in my rickshaw. Their clothes, skin and parts of their heads were in flames," rickshaw driver Fara Ali told AFP at the site of the attack. "It was such a terrible scene."
"We haven't arrested anyone in connection with the bomb attack. But we suspect this is an act by opposition supporters," he said.
Passenger Sushmita Sen burnt both her hands. "I saw a flame in the bus and then I passed out. I woke up to find me and my mother in hospital beds," she said.
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Samanto Lal Sen, head of the hospital's burns unit, said one of the passengers - a 19-year-old boy - succumbed to his injuries today night.
One eye witness, flower shop worker Anwar Hossain, told the country's Daily Star newspaper that he had seen two people on a motorbike near the bus, with the one sitting at the back lighting a bottle of liquid and throwing it through the bus door.
The passengers were the latest victims of the country's deadly protests over the government's plans to hold a general election on January 5.
At least 15 people have been killed and hundreds injured since Monday night, after an 18-party opposition alliance led by the Bangladesh Nationalist Party (BNP) called a nationwide blockade of roads, rail and waterways to protest against the election date.