Trade and Town directories were printed at local and national level throughout the 1800 and early 1900s and these will be kept in Bristol local reference library or local studies library, some, like Slaters, Pigots or kelly's may be available online.
These publications would have given the address and in some cases proprieters of the businesses in a town, sometimes they are listed by trade sometimes alphabetically by name.
The survival of records may depend on the type and size of the business, if it was quite large the business records may have been deposited in the local record office covering Bristol.
Another source may well be the local newspaper archive, also in the Bristol local studies library, and that may well be indexed.
It is also worth nearing in mind that many local business men would likely become involved in the local authority and it would be worth checking any town council records of elected officials to see if his corporate know how found him a place on the council