I think this is a strange watch. Maybe it's not, but I haven't seen one exactly like it.
A little info about it. It says Bulova on the dial and has a Bulova 10AE 17jewel movement with a crescent symbol for 1938 on the movement. The back of the case just has a star symbol on it with the words "BASE METAL." Inside the case back it has the star symbol and 10k RGP BEZEL and a serial number 3768804. I'm thinking it must not be a Bulova case, but it fits the movement like a glove. The crystal measures
19.4 X 21.7 with the 21.7 measurement being measured from the crown side to the other side. The dial is kind of a dark green color although that's hard to tell in my pictures.
That is a strange watch. I like it. Some initial thoughts. . .
I couldn't get a really good look at the star logo on the case, but it is most likely indicative of the Star Watch Case Co. There's a discussion of that company and its association with Bulova in my article on Bulova Case Signatures. However, your watch does not fit the profile of any of the examples of Bulova watches with Star cases addressed in that article.
I have not seen that case/dial combination before. We used to believe that a watch with a base metal or stainless back meant it dated to the 1940s, but recently discovered evidence has pointed to the mid-1930s as when that practice began. For example, I have a 1935 Swartchild catalog that lists replacement cases with steel and stainless steel compositions, and we recently discovered a couple of newspaper ads that show such cases were being offered on watches at that time.
The dial does seem to fit the case quite well, with the numbers and markers aligning with the bezel edge nicely. The case is not a common shape, so I would assume that the dial is original to the case. The style of the dial, with its combination of Roman numerals and dot markers is not typical of the 1930s, but it is not unseen during that time either. I have two examples from 1939 that use some of these same elements. I believe the style of the dial puts your watch in the late 1930s or beyond. It's definitely not an early-to-mid 1930s style.
The 10AE movement is appropriate for a 1930's model. The latest date I have on record for that movement in 1940.
So, the watch seems to hang together as a cohesive unit, appropriate to the 1938 date symbol on the movement. That leaves us with the question of the Star signed case, and, to me, that is what makes this a really interesting watch.
We simply do not know all the various case manufacturers that Bulova used throughout the decades. We do know that Bulova had interactions with Star, although, until now, we have not seen evidence of that in a 1930s watch that appears to be all original.
How sure are you about the crystal measurements? I have not yet found anything that matches those measurements, but there is a known Bulova crystal that is close. That's the G-S Y721, which fits the Regulator, Tildon, Clipper. . . and possibly others. Did you remove the crystal from the watch and measure the inside of the bezel? I have found that method to be the most accurate, although it does leave you with the hassle of gluing the crystal back in place.
I forgot to say something about the dark green dial. That is the one thing about this watch that really makes me raise an eyebrow. We just don't see colored dials in Bulova watches until much later. That makes me think there was a re-dial somewhere along the way. That doesn't mean it's not the original dial and that the dial didn't have those same elements--sans the color--when it was initially finished.
Is it possible that the dial is a very faded black color, rather than green? Or perhaps a gray? Bulova did use black and gray in the 1930s, although the gray was used in two-tone compositions.
I just measured the crystal with a digital caliber without removing it from the watch. And the reason the dial isn't lining up with the case real good in the photos is because I had the back off the watch at the time and was just holding the movement in with my hand and had the back off also with the photo of it on my arm. And the star symbol on the case looks like the star that the Star Case company uses, but usually their cases say Star Case company, don't they? The few I have seen do anyway.
The dial seems unusual to me. I've never seen Bulova use a dial quite like this one. It looks like it might be porcelain.
If you look at the section on Star Watch Case Co. in my Bulova Case Signatures discussion, you will see the star that is on your case. It sometimes appears alone without the full Star signature. I definitely believe you have a case made by Star Watch Case Co.
I have heard others describe a Bulova dial that appears to be porcelain, but I have not observed that in my own collection. I may have just missed it.