I went along as a non-shooter guest on a bison hunt.
In our case,we had a guide with us.We approached on foot to approx. 100 yds from the herd.Point,while there are different styles of hunting,unless you draw a tag for a wild bison hunt,you will likely be guided to a resident herd.The guide has an interest in taking good care of ther herd.So,likely you will be close.
In our case,the hunter could select any bull,but,the bull had to be in the clear.In other words,your target animal must be positioned so there would be no collateral damage.
It was cold,and the wind was blowing.
One shooter used a 45-70 sharps loaded with 405 gr lead bullets.
One shooter had just returned from Afghanistan,and he was a one rifle guy.He used his 16 in bbl FN FAL with 165 gr bullets.308,of course.
And,one shooter had a 416 Rem built on a P-14 Enfield.Why not,if you have a big rifle.
All three were Veterans who could shoot.
One observation,even a very well hit buffalo might take a little while to figure out he is dead.
First buff,45-70.Well hit,penetration to far side hide through lungs.It was a touch astern,due to wind,but a good chest shot.Guide suggested another shot.Good hit.A few seconds and the bull kneed on down.
Second bull,the .308.This gentleman fires double taps well.Thats what he did.Two quick shots,both well placed,animal down.
Third bull,the 416.Big gun.Good hit,animal down...but,another bull horn-coaxed it back on its feet.It was mortally hit,wobbly,but taking steps.No need to let it continue,another shot was fired.Perfect placement,I saw the impact through glass.Animal stood a few seconds longer,went down.
Jump to your own conclusions.I suggest you use a heavy bullet that will expand but not break up.A 200 gr Nosler Partition would be an example. There are other bullets.
I would not worry about pushing velocity to the max.
Study bison anatomy.Look to a book "The Perfect Shot" for one source.Bison organs and bones may not be as you imagine.
Good luck.