Nice watch i am a sucker for a black dial Bully Sweet :)
56 Phantom/black dial
Interesting. I have not seen a Bulova of this era without all the standard Bulova markings on the case back. At a minimum I would have expected to see a date code external. The serial number placement also seems odd for Bulova.
Tentative on the Phantom ID. I'm not so sure about this one.
identically cased 1956 model here http://www.mybulova.com/watches/1956-phantom-5772
That caseback is certainly odd. On two examples, yet. This is indeed a departure for Bulova, especially at this stage in their history, when things are well standardized.
Your comments have generated curiosity and I have looked back with a magnifying glass and I see typical inscriptions but with a very low relief.
Can you see it good enough to tell us what it says?
Between two concentric circles: WATERPROOF ANTI-MAGNETIC down, BULOVA up, other very blurry indistinguishables.
The Mysterious Phantom. Another to add to my list...
I have this watch with the silver dial and the markings on the back are indeed not very deep. Mine says stainless case and all the rest with a very strong serial number in the center. Silver hands and black sweep sec hand.