I wonder whether the saying is somehow related to the tradition of humping the bluey or waltzing Matilda, i.e. humping = carrying a bluey = a swag or bedroll.

That means deciding that you couldn't make it in the city and taking to the roads, in the bush and into small towns looking for whatever work is available. In hard times including the Great Depression this was a viable way to make a living, but a tough way to do it. So the term, Sydney or the bush could mean yhat the alternatives were to be living it up in town, or to be forced to go out to the bush to do it tough, including, for example, if you blew all your money on gambling.

Just a thought.

Helen