Company Names, addresses, dates¹:
  Continental Brewing Co, 512 N Capitol (1897-1901)
  Continental Brewing Co, Alexandria VA

Notes:
I see several brewing companies named "Continental" in American Breweries II², but none from DC or VA. So apparently this was a DC branch of another brewery, probably the Continental Brewery in Philadelphia.
I also haven't had any luck finding anything about "B.B. Baker", whose name is on one of the bottles below.
Charles Fleishman, whose name is on another one of the bottles below, apparently was the DC agent for Baltimore's National Brewing Co before he was the agent for Continental Brewing Co. A Washington Post article from January 18th, 1893 says that Fleishman was being charged with forgery and embezzlement by the National Brewing Co. An ad in the Feb 22, 1902 Washington Post lists Fleishman as the agent for Toledo XXX beer.


Bottles:

(enlarge)	I have a bottle from DC and one from Alexandria. Left bottle is an 8.9" aqua baltimore loop marked: front: CONTINENTAL BREW. CO. / ALEX. / BRANCH / KW / REGISTERED back: THIS BOTTLE NEVER SOLD Right bottle is a 9.2" aqua BIM crown top marked: front: CONTINENTAL BREWG CO. / B.B. BAKER / MANAGER / WASHINGTON, D.C. back: REGISTERED / NOT TO BE SOLD
(enlarge)	This is a 9.3" clear crown-top bottle marked: front: CONTINENTAL BREWING CO. / CHAS. / FLEISHMAN / WASH. AGT. / PHILA. PA.