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