Like ATM machine and PIN number, "mail bag" is a needlessly redundant phrase: mail is the bag.
"post, letters," c. 1200, "a traveling bag, sack for keeping small articles of personal property," a sense now obsolete, from Old French male "wallet, bag, bundle," from Frankish *malha or some other Germanic source, from Proto-Germanic *malho- (source also of Old High German malaha "wallet, bag," Middle Dutch male "bag"), from PIE *molko- "skin, bag."
@dredmorbius thanks! I didn't know about this one.
Generalistic and moderated instance.