Both approaches actually go down the Potomac- since you can't approach from the north due to the no-fly zones, you either come up from the south along the Potomac, or you approach from the west, wrap around the Rosslyn business district (keeping downtown to the northeast) and past the Pentagon to line up.
787s do use the standard gates- passing on Metro's Blue and Yellow lines you can see much of the terminal, I've seen a couple of 787s there recently.
I missed this one earlier, but there's a couple tweaks that run right up my alley.
The Potomac River Visual is what Hellbie is describing and it's kind of gnarly. (Pilots find it fun, passengers less so.)
http://flightaware.com/resources/airport/KDCA/IAP/all/pdfCheck out the third from the last. It literally follows the river.
I've met the guy that did the first set of RNP approaches using monitoring technology to ensure minimum standards of performance as part of Alaska Airlines. He later formed a company named Naverus (later bought by GE Aviation). If you look at the last approach in that pdf, it's essentially the RNP'ified version of the Potomac River Visual. You need specific crew training, authorization, and I believe HUD guidance to fly the approach.
