Green’s Dictionary of Slang

1. (Aus.) an alcoholic’s drink, consisting primarily of methylated spirits.

1935		Mudgee Guardian (NSW) 2 Sept. 2/3: Metho. Recipes [...] ‘Bidgee’ — Methylated spirits and cheap wine (half and half) tablespoon tan boot polish, raisins, a little sugar and water; tobacco if desired to make extra ‘tasty’ and quick-acting. Thi concoction [...] is called Bidgee.
1938		J. Moses ‘Nine Miles from Gundagai’ in Baker (1945).
1946		Longreach Leader (Qld) 14 June 14/5: [as 1935].

2. (Aus.) the Murrumbidgee River.

1993

Aus. Word Map 🌐 Bidgee. abbreviation of Murrumbidgee, often used to refer to the Murrumbidgee River. Often used in discussions about fishing, camping weekends, etc.