It is difficult to calculate time lag between bullet impact to the arrival of the report of the shot. At sea level, sound travels at approximately 1100 fps, slower at higher altitude. A bullet travelling at 1250 fps, which of course is not constant due to velocity drop, out to a range of say 900 yards or 2700 feet, will reach the target in roughly 3.5 to 4 seconds. The sound, which does slow down also, yes, because of difference in air density, wind and temperature and the fact that the force of the vibration is degrading due to friction too, will still arrive after the bullet strike. Why? Because the bullet is supersonic as it leaves the muzzle and the report, the sound of the powder detonation is a millisecond behind the bullet exiting the muzzle, loses ground to the departing bullet until the bullet decellerates to subsonic velocity. Even then, it still has to catch up to the bullet then, pass it.
Just for chuckles, I once took a tape recorder with a microphone by a metal plate at 100 yards and shot the plate with a .22 the time lag was impressive.