I don't see anything in the definition of 'bush' poetry that says it has to be about the bush!! And I don't see anything that says it has to mention 'Australia'. To me, it is simple. Write about Australia or the Australian way of life (which includes city life, seasons, 'Australian' emotions, etc) in a format that has good rhyme and rhythm. If that same poem could fit into another country, and touch a chord, so be it!! There are similarities in every country, if you look hard enough, and it is certainly self-limiting if we were to only write about something that is 'uniquely' Australian. Again, the definition doesn't say it has to be 'uniquely' Australian!!
At the end of the day, as already mentioned by Marty, the word 'bush' is probably a misnomer, but I guess it was a phrase coined back when Australia was largely considered 'bush' or country, with no big cities to speak of.
Me - I write what is in my heart, and personally, I am not overly concerned as to whether people class it as 'bush poetry' or 'rhyming poetry'. It is an expression of what I feel, or a story I want to impart, or even just a point that I want to get across. It is good that we have a discussion on these issues, but I don't think we will ever really find the answers!! (But it is good fun trying!!

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Catchya
IRene