How big of tank and what are all the other tankmates?
Taking the bully out may help. 50-50 chance. Same with cichlids. 3-4 days should suffice. Enough time for the others to establish a pecking order and feel at home.
sorry budd, but I dont even answer some questions on african cichlids, what I dont know, I wont answer. I know nothing about tetras except for what you have already mentioned, ie, moving tank interior around or removing the culprit for a while.