According to
www.coltrevolvers.net , 35,000 Bankers Specials were produced between 1928 and 1943. That site also says the gun is chambered in .38 New Police, rather than .38 S&W. Is that the same cartridge under different names? I know the companies hated to hang the other's name on their own products.
The coltrevolvers.net site is under never-ending construction, but the Bankers Special is one of the few models for which there appears to be a complete write-up. In that production period about 230,000 serial numbers were used up in the series that included the Bankers Special. Is it reasonable to think that one out of every six or seven Police Positives manufactured in that range was a Banker's Special? Maybe. Looks like both .38 NP and .22 LR versions were produced.
There was a really nice Banker's Special up at a recent Greg Martin auction. I was tempted, but I had too much money tied up in bids on other items. If I had won everything I was bidding on, I would have been sunk. So I let that one go buy.
That's a very nice gun you have.