It's looking like a minimum $1500 for a one bedroom rental in Rosslyn, according to the website sublet.com. Way over your desired outlay. I also checked out in Springfield, which is at the end of the Blue Line on the Metro. Far out from DC - probably an hour Metro ride. The cheapest one-bedroom I saw was $700. So...it's pretty much you time or your money. Not a great choice. Hope you find something that works.

 

Don't forget the coffee house strategy.

Go to a coffee shop in the neighborhood in which you're interested and look for flyers of room sharing and the like.

I'm very partial to old town Alexandria. There's always flyers on the fridge at misha's ('greatest coffee you'll ever have' and they're right) offering room sharing group house situations that are often in your price range.