Is this post by you ?
http://forums.gunbroker.com/topic.asp?TOPIC_ID=401178
The only other information I could find about Bartels& Sohn is in a russian forum here:
http://www.huntclub.ru/cgi/bbs/guns?r=85522&l=9270 which looks like a double barrel shotgun made by them which would fit into the time frame of this company given in the other forum.
What I could find out about Wiesbaden, the location of Bartels&Son is that it lies within the Former Duchy of Nassau which was founded 1806 and became part of the Kingdom of Prussia in 1866 so my wild guess would be that "Koenglicher Hofbuechsenmacher" (Gunmaker of the Royal Court) refers to the kingdom of Prussia. Again thats just my guess.
In another post
here I found this quote: "We are told that Hofwaffen-Fabrik would be the Master gun makers place of business and BARTELS was a dealer rather than a maker and had a shop in Zella-Mehlis, a former gun making center." which would indicate that the "bartels&Son" hint is probably something that won't be very helpful in identifying the gun, as a dealer they would probably buy and sell anything and from any time period. But it makes for a good detective case

BTW there are a lot of "Bartels&Son" companies in Germany today, most are financial advisors, maintainance, hardware makers and so on. Nothing I could find that deals with guns.