Definitely NOT Montgomery County. The District as a whole is becoming more bike friendly. There are some great people working on various efforts there to increase the number of bike lanes and possible even incorporate things like sharrows and bike boxes in the future (think Gilliland from WABA and Jim Sebastian over at DDOT). Fenty is a cyclist himself and he takes this issue very seriously. Within a very short period of time we've seen a huge increase in bike lanes all over the city. That being said, the further away you get from downtown, the less bike lanes there are and traffic can get a little more insane. There are some bike routes from Brightwood and down through Petworth, but you've gotta be a bit careful because there is still a fair amount of crime through there. Alexandria has some awesome bike trails, MUPs, and other accommodations, but connecting from this part of VA to other areas around the Metro area can be a bit dicey. I've been biking in and around DC for quite some time and have become a huge fan of the multi-modal commute (a bit off topic, but thought I'd share). Get a folder (which you can bring on Metro at any time) and use Metro to help you connect up to other areas in town. It's the best and most efficient way to travel these days.
DC is a great town to commute by bike. I commuted between Prince Georges County, Maryland and Alexandria, Virginia, 14 miles each way. Most was through DC--Northeast and down along the Mall and across the river to Virginia.
The weather is great for cycling; too. Folding bikes are allowed on the Metro anytime, which extends bike commuting in the winter when it gets dark so early.