Lisa
The way I have always interpreted the term bush was as a general reference to anywhere outside civilisation or more specifically, anywhere outside the big smoke.
There's a bit of a summary about 'the bush' in Australian culture at the following page:
http://www.cultureandrecreation.gov.au/articles/bush/
"Bush" is certainly that but I think it is increasingly replacing related terms. A reflection of the increasing urbanisation of Australia.
When I was growing up it did not seem to dominate conversational reference to the wilderness. "bush" was more commonly used in conjunction with other words
bush mile, bush ape, bush ranger bush mile
When used it seemed to refer to both rural and wilderness areas.
I recall that other words some general and others more precise were used more frequently. So people spoke of the
mulga, scrub, outback, pindan, malee country, never-never and "beyond the black stump".
MInd you this is based on a WA experience and most of the conversations were with country people and city folk of the pre war and immediate post war generation.
As for Lisa's question about including the rainforest as bush, I found a reference to photos on the "The Daintree Bush".
http://nla.gov.au/nla.pic-vn3997786-s51