"It has been a great start but no one is getting carried away. Is it premature to write off Celtic? Yes. Over the last few seasons it has always been close," he said.
"The lead is probably going to be seven points and with three more Old Firm games left anything can happen."
But Bartley is very much looking forward to putting his best foot forward to win another title with the club following their triumph whilst he was on loan in Glasgow last term.
"I still treasure the medal I won last season. It was a fantastic experience and hopefully I can pick up another one," he added.