Anti-government protesters attacked the bus outside the capital Dhaka, the second deadly firebombing in two days, as part of ongoing violent efforts to force the downfall of Prime Minister Sheikh Hasina.
Police said the protesters set the stationary bus ablaze overnight while a worker was on board at Kaliakoir, some 50 kilometres (30 miles) north of Dhaka.
"He was sleeping in the bus at around 3.30 am in the morning when it was torched," Kaliakoir police chief Rafiqul Islam told AFP, adding that no one was arrested.
The opposition also called a 12-hour strike to protest an assassination attempt on Tuesday of one of Zia's longtime aides.
Riaz Rahman survived after being shot four times in his car which was also set alight in an attack the opposition blamed on the government.
Shops, schools and businesses were closed for the strike, while roads were largely deserted as thousands of police and the elite Rapid Action Battalion patrolled the capital.
The violence has now claimed 19 lives since Zia called for the indefinite transport blockade last Tuesday.
Authorities confined Zia, leader of the Bangladesh Nationalist Party (BNP), to her office at the turn of the year after she called for her arch rival Hasina to stand down. Zia remains stuck in the compound.
Zia wants Hasina to call fresh elections following last year's controversial poll boycotted by opposition parties and marred by deadly violence.
