I've not once been asked to show nor have I surrendered temporarily my firearm during a routine traffic stop or on the street.
"I'm licensed to carry and am/am not carrying a weapon today/tonight" is my response. Some states require you to identify yourself as a license holder regardless of carrying so as a matter of courtesy I do just that including when I am not carrying or in states which may not even provide reciprocity with any of the states in which I hold licenses.
I was pulled over for a burned out license plate light and was sent on my way after a brief check. The only thing this state policewoman asked was what I was carrying as she was sending me on my way.
Another situation was in Georgia where at least one of my licenses receives reciprocity though I forgot which one at the time. This was while crossing the street a little later than I should as well as a little further from the official crosswalk than I should but made it across before the traffic light changed. The asked me for my ID, what my hurry was and to be more careful next time.
I had only one instance of a rude unprofessional cop who was a county sheriff with a reputation. He has more than a few complaints against him and the most satisfying thing was throwing him out of the house when he was a "+1" on an invitation after he started acting rude. Beyond that my experiences with local and state law enforcement have been positive whether I was asking for directions, being pulled over/DUI routine checkpoints or when I called them in to investigate some suspicious vehicles on my local airport.
Meter maids on the other hand...
The best advice that's been given is calmly state you're licensed to carry and you either are or are not carrying. This way there are no surprises to them when they see you are a license holder and don't have to ask you. I also would not offer to turn over my weapon to them as there's no reason. Leave it where it is, safe, holstered, cased or however it's being carried. Zero chance for a negligent discharge and if the officer does want it they'll ask for it. I've never been asked.