A number of companies offering discounted bus travel between New York City and Washington DC developed over the past several years. They started as a service for the Chinese communities and are sometimes referred as "Chinatown buses". However as the service has expanded a variety of stops have been added, including other cities as destinations. Also several larger companies have created subsidiaries to enter the market: Megabus is part of international giant Stagecoach (which includes Coach USA), while Boltbus is part of Greyhound.

These companies cut costs by booking over the internet, not offering refunds (although changes are often allowed), and mostly picking up on the street instead of a bus terminal. Several offer very low fares for the first few passengers to book. Many offer on-board Wi-Fi access. In Washington DC the most common stop is at 10th & H streets. Stops called Union Station are actually in that attached parking structure, enter via the mezzanine level (upstairs) of Union Station proper. Most stops in NYC are near Penn Station. Examine the websites below for more information.

Megabus: New York and Philadelphia.

Boltbus:  New York. Besides 10th & H, Bolt serves Union Station and the Greenbelt MD Metro station.

DC2NY: New York.  Does not stop at 10th & H. Stops at Dupont Circle, Union Station, and/or  14th & H. 

Vamoose: Does not serve DC proper, but runs between NYC, Bethesda MD, and Arlington VA.

NYDCExpress : New York and Philadelphia. DC stop is 7th & H. This company is also called Eastern Tours.

Apex Bus : New York, Philadelphia and Union City, NJ. DC stop is 6th & I street.

Dc bus charter: Washington dc ,Maryland, Virginia Bus charter services. 

Of course a wider variety of services are available at GreyhoundPeter Pan, and  Coach USA. Also note that while Amtrak generally costs more, trip times will be one to two hours shorter from NYC than via bus.