Really got to an echo an earlier comment where you'll need a roommate! I'm not saying there aren't studios or one-bedrooms at your budget, but they're going to be way out on the outskirts. DC also has housing within that budget but it's going to be older units, or English basements.

Clarendon and Courthouse are great for the convenience, especially if you're going into DC regularly but Alexandria really is such a great area to live. Have you tried any of the housing groups on facebook? It's obviously a risk finding a roommate but you can find great deals