So I've just been there and back, and I'm posting a bit more info in case it's useful to someone else. The single trip using public transport does take something between 2.5 and 3 hours, and cost in total between $18-$22 (single trip), but is definitely doable and convenient, particularly if you are travelling alone and with not much luggage.
First one has to get from the airport (IAD) to Washington D.C. For these either the Washington Flyer bus (to West Falls Church) or the Metrobus 5A (to Rosslyn) seem convenient. I decided to go for the Flyer bus, which costs $18 round trip (you can return at anytime within one month) and runs every half an hour (on the 15 and 45 every hour). On retrospect, the Metrobus might be a (slightly) better choice, as then I would get at least a chance to “see” a bit of DC since Rosslyn is closer to the center of the city, but anyway.
Either way, now one has to cross the city using the metro, most likely using the Orange line to New Carrollton. Make sure to have small notes to pay for your fare on the machine. How it works is that you look up your destination on a list on the machine, identify the fare that you must pay (chances are that you have to pay the peak fare and add an extra $1 for the paper ticket), select that amount on the machine and enter then the bank notes. From West Falls Church to New Carrollton I paid $6.75 (and the same when coming back).
At New Carrollton you can then take the YTS 921 to Annapolis which costs $5 a ride. This one was a bit tricky, first you have to exit the metro station through the south exit onto a big parking lot. You will see several bus stops, with maps and clearly marked signs of the bus routes stopping there; but 921 does not stop on any of those. It stops at some at some nondescript “kiss and go” area within the parking lot, only some small numbered stickers “921” will give you an indication that this is the place to wait. The small white bus/van itself is also rather nondescript, it may or may not say “Annapolis” on the side. Anyway, the people around and the drivers were typically nice and helpful, so ask if in doubt. It might also come handy to have with you a printed schedule, as this bus doesn't run often, and you might have to wait some time.
The return trip works easy as well, following the same instructions in reverse order. It might only be helpful to know that the bus stops for 921 in Annapolis are similarly rather nondescript, sometimes the only indication is a sign with the YTS logo. Also the bus might be late (once I waited some 10-15 minutes), so allow yourself some extra time for the travel, don't make too tight a plan if you need to catch a plane.
As I said, although it takes a bit of time, the trip is somewhat cheap and convenient. Specially if you are travelling light. I did ask at the counter of the SuperShuttle, but the price for a single trip would have been of $70. This might make more sense only if you are travelling as part of a big party and you can split the costs among yourselves.