The demonstrators, demanding justice and road safety measures, have brought the capital Dhaka to a virtual standstill.
A government minister has accused them of hypocrisy, triggering further anger.
The education ministry has closed high schools across the country and promised to take their demands into account.
However, this did not end the protests.
"They should have taken our demands seriously, but they didn't," Imran Ahmed, a protesting student, told AFP.
There are reports that some of the protesters, mostly aged in their mid-teens, have been checking bus registration plates and demanding to see drivers' identity documents.
"We don't want any vehicles without licences on the streets. Those unfit to drive should not get licences, and we don't want underage motorists driving public transport," protester Mohammad Sifat told AFP.
Some vehicles have been vandalised and police armed with shields and batons have driven the protesters back in some parts of the city.