I photographed a day-long tactical pistol training course and took over 1000 photos. It was routine to get images with empty brass cartridge cases in the air as they were ejected. No motor drive needed. I would try to time the shutter release as close as I could to the gun being fired. In this photo the bullet has just exited the muzzle, the slide has moved to the rear and the empty case is visible but not yet ejected.
This image was shot at 1/2500 sec. and the bullet has a little motion blur that is visible when the photo is enlarged.