You can create an account with coinjar.com.au trading platform and use BPAY or POLi to deposit money from your Australian bank account into your coinjar account.
If using BPay it can take up to 48 hours for funds to appear in your coinjar account. Once your money is in coinjar, you can buy bitcoin. Move your bitcoins from your coinjar wallet to your bittrex bitcoin wallet and trade.
www.btcmarkets.net is another trading platform popular with Australians.