The address was 22A, Queen's Road Central. Contributor 1314 says it "was up an alley at the rear of, I think, Shell House." That matches the map shown on the business card.
The earliest mention of it we have so far shows it called "Victor's Bar", with Jack Conder as the licensee. (Read more about Jack Conder at: http://gwulo.com/node/17492). I'm not sure if it was named after a man named Victor, or if it referred to winning the war.
The 1956 phone book shows it had changed its name to "Conder's Bar".
Some time later, Conder's Bar moved to a new location in Kowloon: http://gwulo.com/node/17488
It is now coming back to me! I remember the side alley location in Central, maybe one over from the Parisienne Grill in the late 50s, but had forgotten the name. I later (c.1960) visited the new location near the Mongkok KCR station. It was then run by ex Flight Lieutenant John? Robbins ex RAF Kai Tak, husband of Joan who worked in Jardine Travel Dept on the ground floor of Jardine House. A very pleasant lady. Shortly afterwards i met my future wife and my pub crawling days were over. Nick