Washburn Prewar Instrument Styles by Pleijsier Hubert is a good source book for Washburn guitar information.
Post a picture of the paper label, any stamp marks burned onto the back center strip and of the bridge. Those things are more helpful for dating Washburns than the serial number by itself. Serial numbers where started over a few times, you need the additional clues to get you in the ballpark.
Ian, welcome to the Forum! This place loves to see photos, many and varied! Maybe take a bunch and post um for us to see what you are fixing? Thanks!
jus'a wildwestern guess.......Sept 1st 1939...better than no guessatall
The paper label in your Washburn was used from 1906/7 - 1915. The serial number A3991 would date your guitar to 1907. It's hard to quit make out but it appears to be a style 115 (see bottom of the paper label). The bridges would typically be Ebony and normally have flattened pyramid wings, this one looks more like one you would see on a Regal made guitar. They also owned Regal Instrument Co. and there was a lot of parts swapping done at that time.
Here is a picture I had handy in my computer from a vintage instrument exhibit we hosted in 07 of my Style 115 Washburn. It has the Ebony, flattened pyramid bridge I mentioned.
This instrument would have been built for gut strings originally. It will be ladder braced and have a bridge plate that is in all likely hood be made from Spruce. The straight across, non-compensated saddle will not play in tune with steel or silk and steel strings. I use Nylgut "Alabastro" strings on mine and they sound and play great, Elderly Instruments has them. Any plastic strings for classical guitar would work though.
Ian, Here are some pictures of original Washburn bridges.
And a couple more.