Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Bhubaneswar to Rome as you normally would.
Bhubaneswar (BBI) is the airport you will fly out of if you book a flight from Bhubaneswar to Rome. You should not have trouble finding flights to Rome from Bhubaneswar; the airport handles an average of 0 outbound flights to Rome per day. You should also have plenty of airline options to choose from since 0 airlines have flights from the Bhubaneswar airport to Rome. It is only a 3.5 km journey to Bhubaneswar (BBI) from Bhubaneswar’s city centre.