I suspect the maker of the bracelet is Oscar Heyman Brothers and that's their secret mark. It would be worth your time to contact them in NY with the number on the bracelet.
Occasionally you find a piece of jewelry with a British Register mark. However since 1884 the registry mark usually has "RDNO" stamped before the number. So Not a registry mark.
On the other side of the pond, the United States has issued patents since 1790, however Patent numbers usually have the letters "PAT" before the numbers. So Not Patent marks.
A Design number is always exciting to find on a piece of antique jewelry, but as you mentioned it was purchased from eBay, I don't think it will be a design number.
Possibly a manufacturing number. More details will help, ie. metal composition, which antique diamond cut, etc.
