means brown barrel. The barrels were browned to keep them from rusting. (Dutch, bus, a gun-barrel; Low German, büsse; Swedish, byssa. Our arquebus, blunderbuss.) In 1808 a process of browning was introduced, but this has, of course, nothing to do with the distinctive epithet. Probably Bess is a companion word to Bill. (See below.)
So, with a band of bowmen and of pikes, Brown bills and targetiers.
Marlowe: Edward II. (1622.)
Brown also means shining (Dutch, brun), hence, “My bonnie brown sword,” “brown as glass,” etc., so that a “brown bill” might refer to the shining steel, and “brown Bess” to the bright barrel.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894