This is the BSW Meisterschaftsbüchse. The design was presented to the leadership of the firm by Engineer Happ on April 7, 1936 as a contender to compete with the popular Walther and Mauser models which had dominated competition match shooting at the time (especially the Mauser ES 340 B and Meisterschaftsmodell ES 350 B, and Walther's Modell 5 and Meisterschaftsmodell).
The fate of the model hinged on its reception at the Versuchsanstalt Wannsee shooting conference that summer, where it was to be presented to authorities for testing. The results of that testing were to determine whether this model would enter production or not. If it were successfully accepted there, it was to begin production on 15 August 1936, immediately after the 1936 Summer Olympic shooting at Wannsee.
It is assumed that the new model was not well received at testing, as there is virtually no further mention of it in the firm's inter-office correspondence. It WAS listed in BSW's 1937 catalogs and advertising, but VERY, VERY FEW examples are known to exist. The most important part that this model played in trainer history (here is the bombshell) is that this model which apparently failed to capture the civilian market is almost undoubtedly the action which was used by BSW to create their first proposal as a replacement of the DSM for the SA. At least three or four were made into military trainer configuration, with one being sent to each of Mauser and Walther and discussed at the joint meeting of the three firms in April of 1938. Compare the measurements of this gun to those mentioned in Jon's Smallbores book in the minutes of that meeting, and the suggested dimensional changes agreed to there in the development of the plans for the KKW. Bingo.
Of the few of these that I have seen, yours comes close to exhibiting all of the features offered for this model in the 1937 catalog.
Steve