I do have a bit of knowledge in this as I have focused on a sniper themed build for hunting.
From my experience the stats which effect the slingbow are Power, +%50 damage at max and Agility +%20 critical chance at max. Sadly neither Dexterity or Control seem to affect it.
Useful related post: https://forum.playboundless.com/t/sling-bow-overview-chart/8327