The Bavarians used the B.A. stamp in most cases, but at some point during the war (1915 I think), they came out with a Hersteller code, similar to the WWII German manufacturer codes. As far as I know (from the examples I have seen), this was only done by the Bekleidungs Depot of the III.b.A.K.. So what you see in the marking is a rectangle intersected in the middle by a vertical line. On the left half is the vendor code and on the right is "B.D.III" over the date. I've seen this on everything from Bluse, to Unterhose, to cartridge pouches and pretty much any other issued item coming out of that corps depot.
Chip