Green’s Dictionary of Slang

1. (Aus./US) a house thief.

1881		Trumble Sl. Dict. (1890).
1895		Crowe Aus. Sl. Dict. 7: Baster, a house thief.
1901		Argus (Melbourne) 20 Sept. 6/4: Among these small fry of the profession may be included the baster or house thief.
1927		‘Jargon of the Und.’ in DN V 438: Baster, A house thief.
1941		Baker Popular Dict. Aus. Sl.

2. (US Und.) a shoplifter [but NB booster n.² (1)].

1919

St Louis Post-Despatch (MO) 16 Jan. 25/1: Where’d you be if I hadn’t planted you, you fat-headed old baster (shoplifter).