The deceased were identified as Barun Kuanar of Keserkela village and Sudhir Mishra of Jharbalangir village.
The bus was coming from Sonepur to Balangir and dashed against the bike at a place under Balangir Sadar police station area.
While Barun died on the spot, Sudhir succumbed to his injuries at the district hospital.
Agitated local residents set the bus on fire, the police said adding, the driver fled from the spot.