Here is some info that will help date it
The trademark "Old Mr. Boston" was first used about 1937.(top left). When it was owned by the Ben Burk Inc. Corp of Boston, MA. Over the years the company changed hands and about a half dozen marks were registered. In the early 1950s- 1970s the mark was owned by Mr. Boston Distiller Inc. and later still in the 1980s the owner was Glenmore Distiller Company of Louisville. If your bottle has any of these names you can probably date it