Green’s Dictionary of Slang

1. a hangman, thus nosey bob v. to hang.

1889		Dead Bird (Sydney) 20 July 3/4: A ‘dull, sickening thud,’ as they say when Nosey Bob drops a criminal off.
1894		Truth (Sydney) 14 Jan. 4/5: George Archer, who was hanged for the murder of Miss Harrison [...] had been shot into Eternity by ‘Nosey Bob’.
1900		Bulletin (Sydney) 16 Jun. 21/1: Despite the probability that the death-sentence will be commuted in the case of the youth Murphy, lately convicted in Sydney of murder, the fitness of the ancient Nosey Bob to continue as official man-butcher is again called in question. Nosey is not particularly anxious to hold on, but wants a pension on retirement, ‘like any other civil servent.’.
1902		Bulletin (Sydney) 27 Sept. 29/1: [A]s the bolt of the drop was stiff [...] ‘Nosey Bob,’ the hangman, had to use a sledge-hammer and much force.
1904		Sydney Sportsman (Surry Hills, NSW) 21 Sept. 1/1: [R]ough, tough, heartless [...] hoodlums, who wouldn’t hesitate to kill an opponent if they thought they’d be able to escape being Nosey Bobbed.
1905		Sun. Times (Perth) 24 Dec. 4/8: I though I got five-fifty a year for finding a ‘Nosey Bob.’ / For hiring a Ketch or a Calcraft, Tommy, a Billington or Binns.
1914		Bulletin (Sydney) 24 Dec. 44/3: ’E showed ’em ’ow to pass out, ’e did. ‘Swing ’er off, yer cow,’ he says to Nosey Bob when the noose wuz put round his neck.

2. an inquisitive person, a ‘nosey parker’.

1930

Listening Post (Perth) 24 Jan. 23: I suggest that space be devoted to the ‘nosey bobs’.