The bus hit a motorcycle near Tukuda, about 20 km from Angul, on National Highway-55 before it fell 15 feet off the bridge, said police. The motorcyclist was among the dead.
The injured were admitted to the district headquarters hospital, of which 18 critically injured were shifted to the SCB Medical College and Hospital in Cuttack.
“We have reports about four deaths and injuries to 36 others. Three persons died on the spot, whereas one died on way to a hospital,” said Angul District Collector Anil Kumar Samal.
The bus was on its way to Athmallik from Angul.
The official said free treatment will be provided to the injured.
It is the second such accident in Athmallik area. On September 9, at least 19 persons were killed and around 25 injured when a bus fell off a bridge.