The Bergstrom Music Co. was a big music shop in Honolulu, (the biggest at the end of the 19th and start of the 20th centuries). 

To start with they sold the production of a few local luthiers; and I have read that this was the shop for whom Martin made its first attempts at making Ukuleles for in 1907.
They were, along with SoCal, one of the two distributors that commissioned Martin to start making steel strung Guitars
As the Ukuleles popularity increased they opened their own Ukulele factory for sale in their own shop and to supply some of the New York Distributors; possibly the west coast ones too. 

One thing to note with Bergstrom Ukuleles is the headstock logo is often on the back of the headstock. This was to allow other resellers to brand the front; or for them to brand the back of other makers Ukuleles that they sold in their shop. I have seen, for example,  they also sold Ukuleles made by Kumalae and you find examples with Kumalae's logo on the front of the headstock and Bergstrom's on the back.