id say the benchmark is 200 proficiency. you're almost there
if youre being cheap on skills and only using the masterwork hunting bow, that's the other reason haha
horse archery is highly dependent on the direction your horse's nose is pointing. it's a little strange to describe, but i find that if i curl my wrist and mouse gradually 90 degrees to the same direction the horse is turning and move it up a tad, that will keep the target in the middle of the screen and at the right height for me to calculate the rest of the relative motion for a perfect shot. maybe ill upload a video of this smooth scrolling.
slow down the horse while you turn, but don't come to a complete stop.
use the sarranid horse. it'll vastly improve your horse archery. coursers are too fast for accurate aiming and smooth turning.
the stronger the bow, the fewer arrows you need to sink to score a kill. masterwork war bow is the way to go, even if you don't get additional power draw to adjust for the accuracy, high proficiencies can fix that.