The most fascinating person in this song is the bloke who isn't really in it --- Billy in the Bowl.
He was, I believe, a celebrated Dublin beggar and robber. He had no legs or severely lamed legs. Someone had constructed a sort of wooden bowl in which he squatted and on which he could move himself about by pushing on the ground with his hands.
If the begging wasn't doing very well, he would flop over and lie on the ground shouting for help. Some kind (and foolish) person would stoop to lift him into his perch, whereupon he would grapple the stranger in his arms (made strong by his endless pushing himself about) and strangle them, then scuttle off in his tub with their wallet, watch etc. So 'playing Billy in the Bowl' came to mean taking someone in a good strong grip, whether for criminal or sexual reasons apparently.