Green’s Dictionary of Slang

(Aus.) an unrestrained attempt, a ‘go’.

1914		Dly Herald (Adelaide) 21 Jul. 4/5: Somebody is said to have called out, ‘Go on, Jim. Get into it. I’m having a bog in this.’ Another man replied, ‘No you’re not.’ The two wrestled together along the footpath to the corner.
1915		Sun. Times (Perth) 29 Aug. 7/2: His contract being completed he determined to have a ‘bog’ in at the Turks, and as he was in the pink of condition he felt sure he had only to present himself to be accepted.