I believe we would all agree that the formal/correct way is, 'bachelor of' or 'master of', and over time, we have discarded the 'of' for a possessive, - bachelor's or master's, for convenience.

Would it therefore be a singular possessive or a plural possessive? IMHO, it would be the plural, since the degree by its very name, draws attention to the collective profile of the persons who are obtaining such a qualification, in this case, bachelors. By such a reasoning, the usage must have shifted to bachelors', and it was but a matter of time from thereon, to drop the increasingly vestigeal looking apostrophe.