my system is the same as Laura's. I've never heard of Jo Kyo Nim. i've heard boo sa bum nim used for assistant instructors. either way it's good that you are preserving korean language in the dojang. i had a conversation with my instructor the other night about bowing at the end of class. he said once he had been visiting a school in the same federation. he was the most senior student present, and was expected to bow out the class. he was tired from class. instead of saying bow to sa bum nim, he said bow to master instructor. as he was bowing, master instructor, excuse me sa bum nim, gave him a sidekick to the stomach and knocked him over.
Are you ok!?!? It was an accident! No really! I promise!