In addition to the esp that fixes bow sensitivity, add these ini tweaks to your Skyrim.ini or SkyrimCustom.ini:

[Controls]
fGamepadHeadingXScale=1
fGamepadHeadingYScale=.80
fGamepadLookAccelPitchMult=1.4
fGamepadLookAccelYawMult=1.4
fGamepadLookAccelSec=.1
fRThumbDeadzone=0.1
fRThumbDeadzoneMax=.97
bGamepadLookApplySnapToAxis=0

[Combat]
fMagnetismStrafeHeadingMult=0.0
fMagnetismLookingMult=0.0
fMagnetismFalloffBorderHeight=0
fMagnetismFalloffBorderMinRange=0
fMagnetismFalloffBorderWidth=0
fMagnetismFalloffExponent=0
fMagnetismInputMovementLimit=0
fMagnetismInputRotationPitchLimit=0
fMagnetismInputRotationTargetMoveYaw=0
fMagnetismMinActorWidth=0
fMagnetismObjHeadingMult=0
fMagnetismMeleeRotationYawLimit=0
fMagnetismMeleeRotationPitchLimit=0
fMagnetismMeleeMovementLimit=0
fMagnetismMaxActorDistance=0
fMagnetismInputRotationYawLimit=0
fMagnetismInputRotationTargetMoveYawLimit=0
fMagnetismSightsFalloffBorderWidth=0
fMagnetismSightsInputRotationTargetMoveYaw=0
fMagnetismSightsMovementLimit=0
fMagnetismSightsRotationPitchLimit=0
fMagnetismSightsRotationYawLimit=0
fMagnetismStrafeMinDistance=0
fMagnetismTargetScoreAngleWeight=0
fMagnetismTargetSpeedMax=0
fMagnetismZeroInputFalloffSec=0



Things these tweaks do:

Fixes acceleration ratios, so you can aim slowly but still turn fast with when wanted.

Gets rid of "stuck" camera. When looking at certain objects/npcs the camera would change sensitivity, not anymore.

Lowers camera deadzone. If your camera starts moving without you doing anything, then increase fRThumbDeadzone by .05 increments until the problem is fixed.

(esp) Makes bow sensitivity match everything else in the game. Now that you have actual control over your camera, you can apply that to a bow.

Removes some "auto aim". Doesn't change arrows or spells, just the camera.