The Native Americans were working on destroying the herds long before the paleface arrived. The paleface just used more efficient tools and the Injuns were too few in number to affect the herds significantly.
A common fallacy is that the Native Americans never killed more than they needed and were careful to preserve the herds of wild animals. In fact, they had absolutely no concept of animal management whatsoever.
Oh yea — herding them off a bluff is a pretty blunt tool when all you want is one per household.