I have serious reservations that the Drilling is a Gesellenstück(Master Mechanic Exam piece), as Bernhard Merkel's trademark is on it. I thumbed thru Schilling makers and did not see one Gerhard Schilling but there was a firm that made/serviced barrel marking machines & the likes under the name of Schilling & Kraemer. But his name was Gebhardt Schilling. So with all that, I hazard a guess that Gerhard Schilling was a firearms merchant and not an actual maker.
I could not be really sure here about this BBF - I had muddied the waters by mentioning my own Drilling then, mea culpa ! -, and my idea was really more of a conjecture than a truly reasoned (elementary?) Watsonian deduction... as I very readily admit.
There are many Schillings in Suhl and also in Zella-Mehlis (even today, e.g. the world-famous Dr.-Ing. Jörg Schilling, probably by now the best and most scientifically anointed grand matter of case hardening anywhere), but I could not find any gunmaker by this name. The Schilling forge, that one yes. But that was a forge.
So it could either be the seller's name of some gunshop anywhere, or a gunsmith, or the gunowner (which was rare on the rib itself, initials or coat-of-arms being preferred then, but it did happen).
As to the italics "B.M.", I am not sure whether the initials would legally qualify as a "trademark". In a Gesellenstück on the other hand, the journeyman-to-be might have procured the raw barrels from a barrel maker, and then put them together. Ot he might even have procured the barrel combination as such from a Rohrschlosser and then have fine fitted it to the system that he had to assemble and tune, which again he had gotten in the raw from a Systemmacher.
True specialists like Axel Eichendorff, Axel Pantermühl (R.I.P. 2024), Hendrik Frühauf, Flintenkalle (Karl-Heinz Pape) or comparable such
Geonim (sit venia verbo Iudaeorum) would be far better able than I, to give a more educated opinion.
Carcano