Dulles International Airport (IAD) is the closest international airport to Bethesda.
Dulles is a major hub for domestic and international air travel with a mixture of legacy and low fare carriers that provide air service throughout the world, https://www.flydulles.com/iad/dulles-international-airport
The distance from Dulles to the National Institutes of Health is approximately 24 miles (39km). This will take approximately 30 minutes in a taxi.
You can find more information about transportation options here; https://www.flydulles.com/iad/travel-information