Hi Toby,
It's a Westfield made bicycle, Columbia was the main house brand of Westfield, and they badged bicycles thus.
Westfield did make bicycles under contract to Sears at times, and they would be badged Elgin in this period, as you say.
The serial number J111937 shows it to be one of the last Westfields made in 1945. The final number was J114781 made 31st December 1945, so yours just a couple of days earlier.
I have seen several thousand of the Westfield BB's from this period, and it is the first with W.S.D. I can only guess it is the owner's initials, or W... School Board, or somesuch.
Can we see photos of the complete bike please?
Thanks,
Best Regards,
Adrian