I think this misconception comes about because most often (IMO) when someone is explaining ballistics, they use the example of the muzzle pointed slightly elevated from flat (therefore, you see the bullet rise slightly, then drop into the target). This is true for long shots (where elevation above 90 degrees is needed) and too a much, much smaller degree for close shots; however, gravity does not take a holiday. It begins to work on the bullet the moment it is no longer supported by the barrel (actually it is even working on the bullet in the barrel, but the barrel puts an equal but opposite force on the bullet--resulting in a additional frictional force; albeit insignificant).
Any physics folks can correct anything I got wrong (it has been quite a while since I did the math).
So in reality, for most shots the bullet does rise slightly before dropping, but this is because of the angle of the barrel not a suspension of gravity.