Take a couple of things into consideration. This airport reminds me of DFW-Dallas/Fort Worth. If you are renting a car, the car rental terminals are offsite, so you must take a free bus there. Add on the time to turn in your car and about a 15 minute bus ride to the airport when factoring how early you have to arrive for your flight. I found the check in and security lines to move relatively quickly. Also, in order to get to many of the terminals you have to take a mobile subway car on wheels(this is the only way I know how to describe it) from the main terminal. This is about a 5-10 minute ride, so factor this in too.
We flew into Dulles, took the Washington Flyer to the Metro, then the Metro to Smitsonian stop and a short walk to our hotel. It was a 2 hour trek during rush hour,after the flight, with luggage. It wasn't the worse thing in the world, but the airport had some sort of "moving lounge" ,the Washington Flyer bus was nice and easy to find, but a long wait and :30 minute ride. The Metro was almost :45, I didn't realize it would take that long.
By far, the nicest airport to fly into is DCA (Reagan National Airport), but it can be a HUGE hassle. Flights into/out of DCA are often very expensive and are sometimes reserved for government officials ONLY, but it is a small airport and a metro stop away from just about everything. If you can swing a cheap trip into/out of DCA, then go for it.
That being said, I recommend flying into BWI (Baltimore, MD) and then taking the metro into DC. It's way cheaper and far less of a hassle, especially if you have someone there to pick you up.
Finally, IAD (Dulles, VA) is an option, but it's normally quite expensive and more out of the way.
SAA flies daily to Dulles, Washington DC from South Africa. The flight makes a stop over at Dakar. It is a very long time on the aeroplane, but you don’t have to catch a connection flight. Flights leave from OR Thambo Int Airport, Johannesburg.
Another option is to fly with Delta, via Atlanta.
You didn't say which day, but there is a 4:50am 5A bus Monday-Fri and the earliest on the weekend is 5:30 from your location (L'Enfant Plaza). As the other poster has said, you will be cutting it really close using the the 5:30 bus to catch a 7am flight at Dulles. I live by Dulles and go out there regularly. You have to also figure in checking in your bags and getting to your gate in your timing and if there are a lot of people at your airline counter. Depending on airline gate location, you may be running through the terminal. Alternative is to take a taxi or arrange a limo service from your hotel. With the distance being traveled from DC to Dulles, both are going to cost about the same.
MY favorite airport here by far is DCA. It is closer to the city and AA has good service here. Paired up with a metro connection and extremely easy access to Alexandria, Arlington or downtown Washington you could easily make a quick trip into the city on a long layover or wait longer before leaving on your next trip out of there.
Washington DC has no airports within its tiny territory, but there are three airports in the surroundings that offer access to DC from either Virginia or Maryland. Reagan Airport is located in Arlington, Virginia, and it's the closest one to DC from all the three, plus you can access this airport by metro (either the blue line or yellow line can take you there). Both international and national flights arrive and depart from there. Its closeness to the city has raised more than one complaint to the inhabitants, due to its proximity to the neighborhoods and the constant roaring of airplanes going to and coming from this place.
If you prefer to take a taxi from Reagan Airport to DC, instead of using the metro, the fare would go around US$11- 20.
DCA is a pleasant airport to land in, indeed. Not only can you walk across a covered walkway to a modern, clean metro system taking you anywhere around the metropolitan area safely, quickly, and inexpensively....but the airport building is a rather pleasant place to be. There are seating areas with loads of daylight windows, a masseuse on duty, restaurants and kiosks that have healthy foods included in their offerings. I've travelled thru DC numerous times over the years and the improvements to their facility and infrastructure of the city continue to intrigue and delight me. These folks know how to move crowds...for sure.
I recommend DC airport highly.
I flew into Balt because I wanted to leave from Balt after Baltoberfest(verrrry wise move). In addition it's cheaper to fly into Balt instead of DC for me. But arriving on a saturday, my options were only Amtrak, or so I thought. The cheap MARC doesn run on weekends. I missed my stop at the Amtrak stations (which is where the MARC station is, unbeknownst to me) and ended up back at BWI on the shuttle bus.
The bus driver told me of another way, taking what amounts to a commuter/city bus to the beginning of the DC subway system. She even had printed out instructions on a sheet to give me and a few others. She said it was only $3, much cheaper than the $18 Amtrack ticket. So I said why not.
In BWI, on the island between the shuttle busses and the cabs is where the city busses stop. You need to wait for the bus #B30 -Greenbelt . Get on, pay $3 in exact change/bills, and sit back for about 30 minutes while you drive thru the MD countryside to a Park 'n Ride where the GREEN line in the DC subway system starts--a place called 'Greenbelt'.
Then when there, go into the station, veer left and use one of the about 8 machines to buy your metro pass for the day, week or whatever. Go up and catch the train waiting for you and you're in downtown DC in about 10 minutes.
Ronald Reagan National Airport is the airport that I fly from the second most. It is named after the 40th president, Ronald Reagan (big surprise.) Reagan National Airport is much closer to Washington DC than Washington Dulles Airport, and is much, much more accessible. It's only a 5 minute Metro Ride from downtown DC. Reagan Airport is split into three different terminals: A, B, and C. A terminal is the furthest south and is the first you come to. B and C are kind of grouped together. This airport is many times smaller than Dulles. Two major airlines that have a medium large presence here are US Airways and American Airlines.
One really nice thing about flying in (or out) of Reagan National Airport is that during takeoff (or landing), there are amazing views across the Potomac River to the National Mall, the Capitol, and the Washington Monument.
This is the airport that I fly out of most often, and it is the largest airport in the Washington DC region. Dulles Airport is about 25 miles west of Washington DC, and is most easily accessible if you take the I-495 Beltway and then the Airport Access Road. Dulles' main terminal has some quite interesting and famous architecture. The airport has the main terminal, and then four further out. The A and B terminals (connected) can be reached from the main terminal by taking an underground passageway; there used to be shuttle buses that connected it to the main terminal, but I'm not sure if those are still available. To reach the farthest terminals (C and D, which are connected), you must take an airport shuttle.
The largest and most prominent airline at Washington Dulles is United, which has a hub here. A good portion of gates in the C and D terminals are all United. Most major American airports can be reached by flights from Dulles; internationally, a good number of European cities have direct flights to the airport. Also, there are now direct flights from Washington to Johannesburg and Tokyo.
Since Dulles Airport is quite far out from Washington DC proper, you must take a bus or taxi to reach the city. However, the Orange Vienna Metro Line may (or may not) soon be extended out to Dulles, making access much simpler.
To fly into DC, you have three choices. The closest airport, and by far the most convenient in terms of its small size and connections to public transport, is Reagan National (DCA). This airport is located in Alexandria, VA, and has a Metro stop right at the airport which will take you into the District. The other two airports are Dulles (about 45 minutes away in Virginia) and Baltimore-Washington International (about 45 minutes away in Maryland). From BWI, you can take a train directly to Union Station in Washington. From Dulles, you have to take a bus or a car.
Driving in DC is a little tricky for the uninitiated. The grid system of the city is not hard to understand, but the major arteries are notoriously poorly marked and it's easy to get lost. When I first moved there, I was constantly finding myself unintentionally shooting off over a bridge into Virginia when attempting to get around the west side of the Mall! If you're a tourist and don't want to stay out too late, the Metro system is easy to use and covers pretty much all the areas you'll want to visit. The Metro closes just after midnight. Watch out for taxis, which run on a ridiculously confusing fare system that is difficult to decipher, resulting in drivers routinely cheating their passengers on fares. If you think you're being overcharged, you probably are--protest to the driver and he'll back down without a fight.