The Studebaker name was everything from carriage builder to cars, trucks, buses, engines for the B-17, military vehicles to even making pocket watches and so on.
The only reference to BF&E, other than the Wisconsin (Milwaukee Rd) rail line, has to do with accounting. Buildings, fixtures and equipment. Could have been a tool tag for that, if they had that department in one of their plants...just a guess.
I’d suggest contacting studerbakermuseum.org to see if they have an answer.