Tom You have already received some very sensible advice on how to administer plastic tape on his bars. All the methods are worth a try but one small item I would advise is whilst pulling the tape around the bar, grip it tight with the other hand and twist it firmly in the same direction thus giving the material an extra chance to "bed" in.
I have always used the same method , wrap anticlockwise in the direction of any movement whilst riding, starting at stem to bar end and tuck in the surplusto be held firmly with bar end plugs .I have never experienced any problems using this format.
Good luck
Doug.Smith
North Dorset
UK