1898
Bike Messenger, New York City 1898
American Distributors Messengers, Western Union Telegraph Co.
1900
From "The Ride to Modernity - the bicycle in Canada 1869-1900" by GlenNorcliffe (p212)
...a group of about twenty teenage messenger boys employed in 1900 by GNW Telegraph Company is depicted. Supervised by some stern-looking elderly gentleman, these younsters had the task of delivering and collecting cables across downtown Montreal on bicycles. Unlike the mountain bicycle messenger delivery services operating in Canadian central cities today, these young men did not have to keep a wary eye out for aggressive automobile drivers, but considerable care was needed when they crossed tram lines and passed horse-drawn vehicles.
Judging by the warped rims and bent handlebars visible in this photograph, several of the bicycles ridden by these messenger boys had seen front-line action on the streets.
~1910
Western Union even had special bikes made up for their couriers. The one pictured above is a fairly standard bike of the 1910's - wood rims, New Departure hubs, wide, motorcycle-style bars. You can see the Western Union enamelled sign in the main triangle. The rack would have stood outside the main office, filled with the bikes of telegraph messengers on standby.
Several board games were produced in the US in the early part of the 20th century, as telegraph messengers became increasingly prevalent. This particular game was based on moving your piece up through the ranks of the messenger company from lowly applicant to owner of the company.
A 1999 paper, "Running somewhere between men and women: Gender in the construction of the telegraph messenger boy", in Acrobat format