I found this:
"Our rub today is the French bistro, or bistrot ---- both are correct, with bistro first appearing in 1884, followed by bistrot in 1892. The origin of the word is uncertain, but the most popular and romantic hypothesis is that it came from the Russian bystro (meaning quickly), introduced by Cossacks during the 1814 occupation of Paris as they shouted for faster service in cafes.

However, this picturesque interpretation is discounted by most lexicographers. They say that the word bistro probably came from Parisian argot meaning "proprietor of a tavern." Another less dreamy version is that bistro comes from the root bistre, meaning a somber and smokey place. "