There is an acute shortage of food and some people are eating uncooked rice and drinking stagnant water to stay alive.
Tens of thousands of people have crowded into temporary relief camps.
The boat incident took place on Friday in the worst-affected district, Madhepura, 150km (95 miles) north-east of Bihar's capital, Patna.
Police said 40 people were saved.
ON Bhaskar, superintendent of police, told the Associated Press news agency: "The boat was overcrowded because people panicked to be rescued and clambered on board."
Angry villagers in Madhepura said they had no idea where to take shelter and complained they had received no food or aid.
"We have lost everything," said Bimlesh Yadav, escaping with his family to a nearby town.
"All our belongings have been submerged in the floodwaters. We are leaving to save our children."
Mohanlal Sharma of the BBC's Hindi service in Madhepura said the road between Madhepura and Purnea districts was under 10 feet of water.
"Along the route, I saw thousands of villagers running towards the town. Some were on foot, some on their bicycles. Some were taking their cattle. Villagers have loaded their entire life's acquisitions on ox-carts and are trying to escape the waters."
Indian PM Manmohan Singh, who visited the affected areas in Bihar on Thursday, said the flooding was a "national calamity".
He has announced an aid package worth $230m (£115m).
But aid agencies say many of the victims are being moved to temporary shelters which lack basic amenities.
A report released by Unicef says there are fears of infectious diseases at the camps.
Army and air force helicopters are continuing to provide aid to the flood-ravaged parts and 600 boats are helping with the relief and rescue work.
But the floods have washed away roads and railway tracks, and water and electricity supplies have been affected in many areas.
"This situation is beyond comprehension," Bihar resident, Arshad Khaqani, told the BBC News website.
The Kosi river flows from Nepal where it is called the Saptakoshi river.
On 18 August a dam on the Saptakoshi burst, triggering the subsequent flooding in Bihar.
Officials in Nepal say hundreds of people there have been hit by illnesses such as diarrhoea and pneumonia and an estimated 50,000 are homeless.
They say nearly 1,000 houses have been completely destroyed. Power supplies and transport have been severely affected.
The costs to the economy are now estimated at one billion Nepalese rupees ($14.25m).
Have you been affected by the floods in Bihar? Send us your comments and experiences.
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