In this particular scenario, it is completely legitimate to inform the officer that your firearm is in the bag; if you so choose, offer that you will be glad to retrieve the weapon from the bag if your state requires "notification of possession". I would not volunteer the bag to the officer, either with the weapon in it or not.
If you hand over the bag, you have volunteered to permit a search of the bag. If you don't want that, don't do it. It is the officer's responsibility to deal with that situation, knowing that his preference will be for you to hand over the bag with all contents. I would not hand over the bag for him to rummage and search if all he wanted was to see the weapon.
And by the way, the permit should be quite enough to preclude the presentation of the weapon itself. I do not suggest lying to the officer, but as long as you are not handling the weapon, he should feel safe, as long as it is holstered and "bagged".
As in most situations like this, relaxed open communications is important.
"The irony of the Information Age is that it has given new respectability to uninformed opinion." - John Lawton, speaking to the American Association of Broadcast Journalists in 1995