Green’s Dictionary of Slang

(US) the hair.

1928		R.J. Tasker Grimhaven 180: I’m heelin’ down to the Sidney Harbour’s for an ocean wave and a work-out on the bonny fair.
1935		A.J. Pollock Und. Speaks.
1946		St. Vincent Troubridge ‘Some Notes on Rhyming Argot’ in AS XXI:1 Feb. 46: bonny fair. Hair. (Origin uncertain, but probably American.) This is certainly a mistake. The word in rhyming slang is Barnet Fair, named after the most famous horse fair in England, held at Barnet, in Hertfordshire, for four hundred years.
1960		(con. 1950-1960) R.A. Freeman Dict. Inmate Sl. (Walla Walla, WA) 15: Bonny-fair – hair.