Company Names, addresses, dates:
  Rother's Vinegar Depot, Green Street, Georgetown (1845) ¹
  J. Rother Georgetown Vinegar Depot, Corner Green and Olive Streets, Georgetown (1846) ²
  Rother's Vinegar Depot, w side Green near Bridge, Georgetown (1853) ³

Notes:
The building at the corner of Olive & Green Streets (modern day Olive & 29th NW) started out as Rother's Vinegar Depot. I'm not sure what a "Vinegar Depot" is, but at some point it became a Bottling Establishment. About 1854 it was bought by Arny & Shinn, then in 1862 Arny retired and it became Riley Shinn's Union Bottling Depot. In 1871 it was taken over by Palmer & Green, and Mr Green dropped out in 1874, so it was the Samuel C. Palmer bottling establishment until about 1892. ⁴
There is not much information about J. Rother, or his vinegar depot. I can't find anything about him in the U.S. Census, and I can't find any indication that he bottled soda, other than the fact that there exist bottles embossed with his name on them.
Besides the bottle I own (shown below), there are other examples that are the same size & shape, but some are different colors. From the shape and color of the bottles, they are beleived to be made by the Baltimore Glass Works (1799-1905).


Bottles:

(enlarge)

This is an 8.5" yellow-olive colored torpedo shaped bottle with a tapered lip. It is embossed: veritically on the side: J. ROTHER