I'm going to DC next Monday and hope to visit the new museum. One of my biggest problems is that it closes at 5:30 every evening. I don't arrive (at Reagan) until almost 4 next Monday, so there's little chance of making it out there in time. My training will last until about 4:30 every afternoon, so again, there's little chance of getting there in time. I fly back Friday afternoon.

According to the Washington Post, there is a shuttle bus available from the NASM on the Mall to the new facility. It costs $7 for the round trip. As Mary Anne pointed out, it's also possible to take the Metro to the closest station to Dulles and then to take a bus the rest of the way. You could even take an airport shuttle from Reagan to Dulles, but that wouldn't make a lot of sense, at least in my case.