My black bear success is very limited to a single small bear. However I like the advice of the Manitoba outfitters I've used.
Black bear die faster from a well-placed arrow than a bullet. Black bear blood clots almost instantly(they would have killed each other off if it didn't), so if an arrow stays inside the vital zone, it makes another cut whenever the bear's leg moves. A bullet makes a single hole, and if it isn't a perfect hit, the blood doesn't flow for long. If shot by a powerful bow and the arrow passes all the way through, a bow isn't any more effective than a bullet.
On my last try, the only bear that didn't go 30 yards was hit in the heart with an arrow which almost bisected the heart.