I bet if you really wanted to find a way, you could have taken it out and put it away with no one knowing.
Try keeping a hand towel in the car. You can cover stuff up easily; use it to pick up and hide the gun (or something else); and it can come in handy if something spills, or the seat needs to be covered for some reason. I always keep a couple of good quality towels in the car.
(If you have to change a tire, you can use it to wipe sweat or Goop off your hands and face. If it is dead winter, you can cover your ears or head if need be--yeah, it would look weird; I'm just making the point that keeping towels in the car is a good idea.)