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