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