The accident occurred near Misia village under Bind police station area when the driver lost control of the vehicle, District Magistrate Thyag Rajan said.
The bus was straightened with the help of three cranes, the DM said after visiting the spot.
The driver and his assistant have fled from the spot.
Two of the critically injured have been referred to Sadar hospital in Biharsharif while remaining 20 got treatment at a primary hospital at Bind, Rajan said.
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