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