John Williamson recorded a song called BUSH TELEGRAPH. It's on 2 of his albums: "Pipe Dream" (1998) and "We Love This Country" (2005).

I haven't seen a formal definition, but I get the impression "bush telegraph" is Australian slang for any informal way of distributing news or rumors. "I heard it on the bush telegraph" is equivalent to "I heard it through the grapevine."

Bush Telegraph is also the name of a radio program on ABC (Australian Broadcasting Corporation). I think the slang expression came first, and the radio program was named after it.

So nowadays when a person says "I heard it on the bush telegraph," I suppose they could mean "I heard it on the radio."

I doubt that the song is meant to refer to the radio program, however.

Anyway, you can hear an excerpt from the song at we7.com. I transcribed this from that excerpt:

There's rumor of a gold strike to the south of Ballarat,
And someone stole some cattle at the back of Carly's flat,
And there's been a fight in Denny Ryan's bar at Ararat.
You heard it on the bush telegraph.
Fat lambs brought a record price last week in Bendigo.
Tommy Burka's been to mass three Sundays in a row.
It used to take a family death or ... to make him go.
You heard it on the bush telegraph.
We don't....