Some copper alloys have a tensile strength comparable to those of the more common low-alloyed steel (which is used in many bike parts). The E-modulus is in the range of titanium and about half that of steel, so a copper tube is twice as flexible as one made from steel with the same dimensions. Also, i imagine finding copper tubes in the dimensions needed for a bike handlebar might prove difficult, so copper-plated steel part is more feasible, if you want the looks. I doubt it will stay shiny for a longer time, copper oxidizes fast.