I would suspect that Bell had some feelings about wounded and suffering elephants and that he probably wanted a quick kill. I doubt that he wanted to constantly face wounded and suffering elephants. It did not improve their disposition. I would not want to face one, even armed with a 416 Rigby, or some other big rifle.
I go back to the famous video of Game Rangers shooting animals - a representation of how poachers do it. They seemed to fire two quick shots, if I recall properly, but every animal dropped like lightning - instant death. Rifles were FN-FAL types, undoubtedly in 7.62 x 51 NATO caliber. I suspect that an elephant is like any animal. If you have no fear of it, hence are willing to get close, and know precisely where to shoot it and have the skill and calm to produce those shots time and time again, that you need a lot less gun than most of us would, who are guarding against the condition of shooting a charging elephant, or one that tricked us because we didn't know the nuances of its behavior.
I personally wish it was never desired or necessary to shoot one of those intelligent, magnificent animals, but I know that is not realistic from a Game Management standpoint, and I have nothing against legal hunting if the animal is used for food or other purposes, which I believe they are when given to local residents of the area after a trophy is taken. Just not my cup of tea.