Flying to Chitwan from Kathmandu ensures that you spend as little time traveling as possible. With a flight of less than 1 hour, you can be in Bharatpur on your way to Chitwan National Park before a bus would even get out of Kathmandu Valley.
The flight departs from Tribhuvan Airport in Kathmandu. This is likely the airport where you arrived in the country. There is a domestic terminal specifically for flights within Nepal. Flights to Chitwan go to Bharatpur Airport.