Both destinations are served by Gaya (GAY). Since there's no flight route between them, the best way to travel is by road.
Chatra
Fly to Gaya (GAY), then travel by road to Chatra. Taxis, buses, and private cabs are available from the airport.
Bodh Gaya
Fly to Gaya (GAY), then travel by road to Bodh Gaya. Local transport options include taxis, auto-rickshaws, and state buses.