I found this old DC directory from 1903. One interesting thing is that there are only 9 merchants listed under Automobiles (including the American Cycle Manufacturing Company, and thte Washington Electric Vehicle Transportation Company) and 64 under "Biycles and Sundries." A lot of these are just individuals listed by name (neighborhood mechanics?). But there are a few bicycle shops listed. These include:
Acme Repair and Bicycle Co - 1749 Pennsylvania Avenue NW
American Cycle Manufacturing Company - 819 14th Street NW
GPO Bicycle Repair Co - 33 H Street NW
National Cycle Works - 904 G Street NW
New York Bicycle Company - 424 9th Steet NW
The last two of those are, respectively, where the MLK library and J. Edgar Hoover buildings are today.