I believe this to be a Bulova ORD Dept watch. Although the case back has been ground smooth, when you look at the inside of the case back at the right angle to the light, you can see the "ORD DEPT" and "USA" as a very faint reverse stamping.
Capturing the "reverse" stamping on my camera is really tricky. I thought it was a "military issue" type watch until I removed the cover and noticed the impression in the metal (and a chance encounter it was too!).
I'm going to try and get a photo of the inner case that is good enough to show the stamping. I suspect that many other A-11 or ORD owners might be surprised if they removed the dustcover and held it at an angle to the light!
I've added the another photo that shows the inner face of the dustcover. I've flipped the image to make it easier to read, but you can see the ORD DEPT stamping quite clearly.
Using the Mk.1 eyeball, you can also see the "U" of USA and the "OF" below that. The BULOVA WATCH CO stamping is clearly there, but not easily destinguished even with the eye. You can just see the "pattern" that the stamping makes.