Marcus Goodrich in his novel, 'Delilah' describes the ship as being bluish-gray with rust red decks. The Delilah was an early destroyer operating in the Phillipines in the years leading up to the US entry into WWI. Goodrich himself served on the USS Chauncey, a sister to the Bainbridge. The Chauncey was sunk in a collision during WWI. 'Delilah' was published in 1941 and acheived critical success at the time. For a while it was on the required reading list at the Naval Academy. It is not a novel of great naval actions, rather an investigation of interpersonal relationships between officers and enlisted.
So, that is a bit of eye-witness storytelling. Take it with whatever sized grain of salt you want, considering the Asiatic Fleet versus the home waters and 1917 versus 1902.
I have heard about the red decks (they were steel, not wood) before and have seen them on some period colorized postcards.
Next is Eric Ronnberg's excellent monograph "Paint and Colors for American Merchant Vessels, 1800-1920: Their Study and Interpretation for Modelmaking" from the Nautical Reserach Guild
http://www.naut-res-guild.org/nrg_colors.htm
Read the article. it has some very good information on color theory as well as some concepts of scale color.
Ignore what is says in the title about merchant vessels. While the article draws heavily on commercial building and railroad painting practices, the concept of getting the most coverage for the dollar will be as attactive to the shipping tycoon, railroad tycoon, or Bureau of Construction and Repair
I have heard the color applied to some early destroyers a Bottle Green. Consider the following plate in Ronnberg.
You can see that the Bottle Green is very dark and would appear black in old B&W photography.