do you just let the bow fall and be caught by the sling
Correct
The hand is the only true contact point with the bow,therefore you want your hand to influence the bow as little as possible, you want as little hand contact on the grip as possible, using a relaxed grip on the bow.If you whiteknuckle grip, or straight stiff finger the grip then the hand is not relaxed, let the grip rest in the hand from the lifeline in the palm to the thumb. I find the sling to be a mental thing for me, its just there to reasure me that the bow wont drop to the floor.
If the bow falls after the shot then you have accomplished the proper grip shot form, if you grab the bow by reflex after the shot the chances are that you are grabbing the bow before the arrow has completly left the bow therefore you have altered or effected the flight of the arrow.