Out here in the West , our bears must be the small country cousins to what you guys hunt back east. The last bear I took was in 2015, weighed 315# field dressed, and fell to a double tap from a 10mm Glock and 200 grain Hornady XTP's. I shot him twice because we were hunting Oregon's Coast Range and I did not want to risk the bear disappearing into the impenetrable rain forest. He staggered 17 feet, fell, and was dead in the time it took my nephew to smoke a cigarette.
After reading this thread I went back through my hunt notes. In almost 40 years I've killed 31 black bear. I used a .270 Winchester, a .35 Whelen, and a .45-70 for 3 of them. All the others were handgun hunts- 10mm, .45 Colt, .41 Mag, .357 Maximum.
EVERYTHING I know and practice about hunting boils down to putting the bullet in the right spot for a humane, fast kill. Bear, like almost all other game species in North America, are not hard to kill.
And to the OP:
Perfect your accuracy load and practice precise shooting with it. Learn where the vitals are on a bear so you can shoot into the vitals EVERY time, from any angle. Quit worrying about making 2 holes- your efforts should go toward making 1 in the right spot. Get to know your weapon and your load so well that you KNOW it will be a good shot, and you will know when NOT to shoot.
Good Luck!