Cart before the horse. You have no evidence that the BB is the cause of the click, and in fact it's very rare that it is, and unless the shop already addressed the other possible causes neither do they. In probably 99% of the cases it's a loose part - crank, pedal, chainwheel bolts or the part securing the BB into the shell. Indeed if they replace the BB the click may go away - because in the process they will normally tighten most of those items.
Creaks, Clicks & Clunks