No import code on movement and no "International" designation on dial. Non traditional case back design bears non-US traditional s/n.
Can you provide a photo or confirmation of text (if any) on the inside of the case back?
Without an ad, based on provided photos and all other contributing factors, I would call this one a
1963 "International"
produced in Europe and offered for sale outside the US.
There may be an import code on the balance, which is covered by the rotor, so will need to look there also. I agree, it could be an international model, and there may be a case number inside the back as well. I did not find a match in the available ads. Unknown model at this time, waiting for additonal details.
I believe some, if not most Bulova's sold to the international market still had a standard model name.
For this watch, I believe it is part of the Bulova Date King series. Whilst not the watch shown below, the subject watch has similar features.

I just noticed the 'Bulova International LTD' on the caseback. Looks to be a non-USA model, and can be placed under the International model name.
In reply to I just noticed the 'Bulova by Andersok
At this point; that's my line of thinking as well, Ken. If it's marked as "Bulova International", with the non-standard back markings, it was produced somewhere besides the US for the market where it was produced.
It may very well have a name but could also just have a number designation. Without a database of European ads, the best we can do for now is list it as "International" and keep all similarly marked watches in the same "drawer" for now, unless a "spot on" US ad appears . In that case, it should still be cross referenced "International (US model name )". Those are my thoughts.
Just to add that we have seen adverts for these internationally sold watches with the same model name as sold in the US.
In reply to Just to add that we have seen by mybulova_admin
Agreed, Stephen.
Panel - are we agreeing on "International"?
In reply to Panel - are we agreeing on by Geoff Baker
Agree
For now - agreed.