Green’s Dictionary of Slang

(US) to rush headlong, to charge at; to drive fast.

1963		A.E. Morgan Six-Eleven (1966) 240: Keep an eye out for the signal [...] If it’s green we go barrel-assing.
1968		G. Cuomo Among Thieves 296: Delft was barrel-assing toward the other end and not even looking.
1975		E. Torres Carlito’s Way 33: Where yo’all barrel-assing to?
1989		H. Rawson Dict. of Invective (1991) 26: barrel ass, to. To move fast, especially when driving.
2001		S. King Dreamcatcher 80: Henry could go barrel-assing down the road at sixty.