Banerjee also directed the district authorities to put up speed restrictions on the road.
The bus had rammed into the bridge early yesterday and fallen deep into the canal.
The bodies of 41 passengers had been found so far from the canal. Eight people are believed to have been injured in the accident.
The chief minister, who had visited the spot soon after the incident and stayed in the town overnight, said the condition of the bridge had to be examined.
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The state government had announced compensation of Rs 5 lakh to the next of kin of each of those killed and Rs 1 lakh for those gravely injured. Others injured would get a compensation amount of Rs 50,000.
Banerjee said the district magistrate had already handed over the compensation to the kin of those killed.
"We had completed handling over the bodies to their family members by midnight," she said, referring to the 36 bodies that had been pulled out yesterday.
On the possibility of more casualties, she said, "We have to check. They (rescuers) are looking into it."
Murshidabad district magistrate P Ulaganathan had earlier told PTI that there was no confirmation on the total number of passengers travelling in the bus but it was estimated that it may have been carrying some 50 people.