Well I have to say the idea of taking bear with a 6.8 is new to me. I have read the story and it is legit, but before I step away from this one for good, I wanted to give everyone here some parting knowledge concerning the mechanics of terminal ballistics.
Rapid death is brought about only by brain death (i.e., the collapse of the central nervous system). Brain death can be caused directly by damaging the brain or upper spinal tissue, or indirectly by depriving it of oxygen. Oxygen deprivation is the result of cardiac arrest or of hemorrhaging which reduces blood pressure or damage that completely shuts off the circulatory function. Thus rapid death is accomplished by causing the collapse of the central nervous or circulatory systems. The single most important factor in wound lethality is bullet placement. This cannot be overstated. It is true that sometimes a direct hit on the brain by a bullet is not instantly incapacitating but generally this is because that portion of the brain struck is the relatively "unimportant" part associated with cognition. Hits against the base of the brain or the upper spine are almost always instantly fatal because these regions control the involuntary vital functions like heartbeat and respiration. In the case of hemorrhage resulting from damage to the lungs or arteries, brain death will likely occur prior to cessation of cardiac function; the time required for brain functions to deteriorate to the point of unconsciousness depending on the rate of hemorrhage. However, when damage is done directly to the heart, the circulatory function may be arrested first, leading to unconsciousness within a few seconds. There is another mechanism of cardiac arrest that is less well understood but which may account for the nearly instantaneous death of game animals hit with modern weapons and that is induced cardiac fibrillation and arrest. The precise mechanism for the onset of the cardiac arrest is not fully understood, but its effect is well documented. It may involve some type of local neurological or humeral communication between the heart and lungs that gets short-circuited. Alternatively, a violent wound to the lung tissue may create a tiny embolism that interrupts cardio-pulmonary function at a critical moment. Other than hits to the central nervous system (brain and spine) or the unpredictable mechanism of spontaneous cardiac arrest, the only reliable cause of rapid death is through hemorrhaging produced by cutting a hole through major blood-bearing organs (heart, lungs, liver) or major blood vessels (e.g., aorta). The dimensions and especially the location of the cavity produced by the bullet will determine the rate of hemorrhaging and in turn the rapidity of the onset of death. It is actually more lethal in some cases to sever the arteries directly above the heart, than to penetrate the heart itself. If these arteries are cut, blood pressure instantly drops to zero and death will follow in seconds (this is one reason why an arrow can kill as fast as a bullet). Lethal hemorrhaging does not depend upon how much blood exits the body, but only upon the loss of blood pressure. A bullet which exhibits both expansion and deep penetration is desired. Three things are worth noting: 1) hemorrhaging in the thorax is far more severe in the case of pneumothorac injuries (collpased lung) than in vascular tissue such as muscle, due to the relative pressure difference between the pleural space and the cardio-vascular system, 2) the surface area of the wound, not its volume, is most related to the rate of hemorrhage, and 3) the body's natural response to hemorrhage, coagulation, is more pronounced in extremely violent wounds which rupture thrombocytes, releasing fibrin into the blood (in other words very sharp cuts generally bleed more freely and longer than ragged, macerated wounds - although a cleanly severed artery may spasm and close, whereas a torn artery may continue to bleed).
The first hit is the most important, because endorphins that are released into the body as a result of serious injury cause the constriction of the blood vessels, reduce or eliminate most pain, and condition the body to operate with minimal oxygen in the blood. If the first hit is not immediately lethal, then subsequent hits will often be less effective in quickly dropping the target, even if they are lethal wounds. Few people realize this, but it is well documented. It is the same mechanism which makes a startled or alert deer harder to kill than one which is completely surprised, because fear also triggers the release of endorphins. It is sometimes advised to go for a "mobility kill" (in military parlance) in order to prevent or stop a charge, incapacitate an armed aggressor, or to prevent a wounded animal from escaping. Mobility kills are hits which prevent or limit movement, and on game are usually aimed at the front shoulder. If you read the exploits of African hunters you will find that when the first shot against a dangerous game animal failed to drop it instantly, the second shot was sometimes intended to physically immobilize it (it is worth noting that some very reputable hunters argue against this approach). Once immobilized, it could be dispatched with a precise shot to the brain. Against humans, the hips are the target. According to Louis L'Amour, this was the preferred target for some gunfighters in the Old West, because the hips are the center of movement, therefore easier to hit, and because a bone-breaking hit here would put a man down. Partly for this reason, the power to smash major bones is also sometimes an important attribute for a bullet load.
If it were me i'd er on the side of caution because all it takes it that one time that bear gets a little too close and doesn't go down from the first 2 or 3 shots from the 6.8 and you find yourself waking up in a hospital or worse. "It's better to have and not need, than to need and not have."
Casey