Should be pretty simple, In general when a bow string is pulled it is tight V shape, for that you can setup a two bone rig with stretchy bones. You can try mixing in Spline Ik for that extra control.
if you want to keep it really simple, An FK setup with 3 bone joints would work, after all it would be the hand ik handling everyting in your animation and not the bow string.
Goodluck