J. Bates was an assayer located in Colorado Springs, Colorado. Although there is a "miner" listed in the Cripple Creek Directory of 1895 of the name J.B. Bates, he is not listed by 1900 or later and is an unlikely candidate.
The J. Bates of Colorado Springs is listed as running a laboratory in 1902 — after 1900, assayers were listed under the heading of "laboratory." He is listed in 1902 at 1202 S. Nevada, in 1903 at 1622 S. Nevada (under Laboratory), and no longer listed in the 1904 and 1905 directories.
Since Colorado Springs is only 37 miles from Cripple Creek (two hours or less by train), he very likely served as the assayer for Cripple Creek miners.