Bullets don't always work the way you would like. Multiple hits up close are a must. He doesn't need to just hit. He needs to hit faster than the BG does, and there is a good chance, the BG will hit at close range. So the question becomes "How fast can he hit?"
I can't tell you how exactly how many rounds it will take to put the BG down in his next future gun fight. I can tell you it will most likely be more than one. Make him train for it.