The Telstra bill that I get only mentions credit card payments, for which there is a fee, but not debit cards.
The only way that I can see to pay by debit card is through PayPal. That would avoid any fee, if applicable.
Does anyone know how PayPal might react to lots of small transactions going through? I wouldn't want to risk a PayPal account being closed.
Just select credit card payment on the 'pay my bill' webpage of Telstra and enter the Bankwest card details. It might be a debit card, but Telstra just accept it as a Mastercard (or whatever it is). So it's certainly working for me - to the tune of 50 transactions a day x 2 accounts.