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