- I think we have a bush rat living at our place in suburban Bexley, Sydney. He is nocturnal, shy, has nice glossy coat of light reddish brown with white underbelly. Sweet face. I've never seen a sweet face on a black rat. And his tail doesn't seem as long, scaley and sinister as a black rat. I've clobbered plenty of black rats but this wee chap fails to incite my rodent rage. He's been here for 3 years, spotted around 10 times, usually late evening. Could a bush rat be living in an urban area? Our place is quiet with lots of trees. We also have a family of blue-tongue lizards.