Green’s Dictionary of Slang

a dustman (cf. dusty bob under dusty adj.¹ ).

1834		‘Guess the Rest’ in Flash Minstrel! in Spedding & Watt (eds) Bawdy Songbooks (2011) I 106: Every one could spy / What she had been about. / She’d with dusty done the trick /[...] / In fact, she’d had too much —.
1836		London Dispatch 13 Nov. 70/1: ‘Dusty Bob’ and his ‘Oss’ — A flying dustman [...] was brought before the Lord Mayor, charged with having stolen a bottle of champagne.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor II 178/1: Father vos a dustie.
1877		‘The New London Cries’ in Laughing Songster 109: Then Dusty and Crusty with voices so lusty.
2003		McGill Reed Dict. of N.Z. Sl. 71: dustie Dustman or garbage collector.