Eugene, This is NOT "Capt" Billy Bush at all. "Capt" Billy was born in 1746 in Orange/Spotsylvania Co., VA and died in 1815 in Clark Co., KY. He was the son of Philip Bush and grandson of John Bush - therefore - the great grandson of Abraham.
I do not know who the William Bush might be from your query. Do you think he might be related to your Bush line??