According to Goins Encyclopedia of Cutlery Markings:
A.W. Bradshaw & Sons Germany c. 1856-1860
Albert Bradshaw was an importer and manufacturer's agent for all types of cutlery. The firm was at 48 Maiden Lane, New York City 1856-1859. In 1860, they were at 18 Platt."
This firm is listed on strazors.com as possibly linked to the Kastor/Camillus/Imperial cutlery empire. Possibly as one of the trademarks or companies that Kastor bought out over the years.
http://strazors.com/uploads/images/articles/kastorlist.pdf
http://strazors.com/index.php?id=321&doc=adolph_kastor_koster_1856_1946_
The knife is very old and shows a ton of wear. It is some sort of slicer that has been steeled to within an inch of its life. The handle does not look to me to be original. I think that the original was probably closer to flush with the bolster. $10 is a good price for it. I wouldn't have paid much more than that for it. Because while it is very old and kind of cool, the condition is pretty awful and there isn't a way to restore it that adds metal back to where it is missing. It is not a knife brand or profile that is in high demand. If I had this knife, I would probably just sharpen it and use it. You won't hurt its $10 value by polishing it or sharpening it or putting a new handle on it. But you probably wouldn't help it much either.