That knock back effect as in a railroad engine car hitting a bear wouldn't occur even with a 50 BMG round, shooting a 50 caliber 750 grain bullet at 2700 fps. Any time a large (300+ lb) game animal does the acrobatics thing at the time of bullet impact, it's not because the energy of the bullet moving the mass of the animal. It's due to the animal's nervous system and muscle response to the bullet impact. Believe me. I have shot a substantial piece of birch firewood with a .460 Wthby before, and it didn't even knock it over. Range ~ 15 yds. Birch log was about 22" long and 16" in diameter.
Mythbusters rans a show on the 50 BMG hitting a human dummy to see whether or not the impact of the bullet against a solid steel plate placed in the center of the chest cavity would throw the human dummy backwards and to the ground. Never happened, even with the bullet not penetrating the steel plate planted in the dummy. Very unimpressive. After seeing that you'ld want to take a bazooka out bear hunting.
The bright side is that that isn't how bullets kill animals, so you dont need the pile-driver force. Bullets kill game by short circuiting their nervous system when it comes to the instant death kills, or by damaging vital organs, creating massive blood loss, loss of blood pressure leading to unconsciousness, and in short order - death.
You go bear hunting, you better go on a guided hunt. Something on the show you watched has evidently gotten you good and spooked.