So far as we know, batfowling was never an American sport.
Perhaps game has always been too plentiful. But we have to go way back to this ancient practice in the fifteenth century for the origin of this expression.
Batfowling was nothing more than the hunting of birds at night, the hunter armed with a light with which to dazzle the sleepy birds, and a bat with which to kill them. (The next day they formed his repast, ba-ked in a pye!)
Or, in some instances, the hunter would use a net for trapping the birds, hiring a boy or someone else, armed with a bat, to stir up the birds asleep in a bush.
The birds, attracted by the light, would fly toward it and become entangled in the net. When there were more birds in a flock than could roost on a single bush, the batfowlers usually beat the bushes adjacent to the one on which the main flock was asleep, thus literally beating about the bush to reach their main objective.
So when today Junior says, “Daddy, are you going to use the car tonight?” we recognize that, like the batfowlers of old, he is “beating about the bush,” approaching indirectly the subject he has in mind.