Hi! My boyfriend and I, plus our dog, Theo, are also looking to rent under the same conditions as you and your girlfriend; however, we would really like find a place with a fenced in backyard for Theo, but it is out of our price range. My boyfriend is beginning a PhD program at College Park this fall, and I'll be working and (hopefully!) starting grad school next year. So, if you and your girlfriend are still looking and could entertain the idea of sharing a place with Neil, myself, and Theo, then let me know ASAP (bojam00 at gmail dot com), because we could rent a bigger, better place for $2400--i.e., $1200 (you) plus $1200 (us).
To give you an idea of the possibilities, I've found numerous houses/townhouses that have anywhere from 3-5 bedrooms and 2 baths in addition to a basement, a driveway and/or garage, and fenced-in yard; prices generally range from 1750-2400 (click here for an example). Utilities are generally not included and usually run $100-$150, though this varies by size. I don't think a bike is necessary for commuting around the city if you live within walking distance to the metro (which is a necessity for us).
If you would like more information, contact me (info above) and I can give you a better idea of who we are and some of the places I've found that fit the above description.