Cr Rudge was absent on Wednesday night when councillors considered a report by general manager David Sherley that offered two options - either dropping the idea or further exploring the option of a popularly-elected mayor.

Deputy mayor Bobby Bourke, who has spent the past decade trying to gain support for a referendum on the issue, called for a further exploration of the issue and won support from councillors Jess Jennings, Alex Christian and Ian North.

But Cr Rudge's absence meant the final vote was four-four, with mayor Graeme Hanger using his casting vote to defeat the issue. For now.

Cr Bourke told the Western Advocate on Thursday that he believed all nine councillors should vote on the proposal to hold a referendum so he would bring the item back to the July meeting of council through a notice of motion.

And Cr Rudge, who was elected to council on Cr Bourke's preferences, told the Advocate she would likely support the proposal, finally giving Cr Bourke the five votes he needs.

"Bobby and I went to the election supporting a referendum and I think it's important for the people of Bathurst to finally have their say," she said.

"I do see some negatives [with a popularly elected mayor] that concern me but if it turns out that the people want it, then that's what we're here for - to represent the people of Bathurst."

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Cr Monica Morse spoke against the idea of a referendum on Wednesday night, likening it to the United Kingdom's Brexit vote and suggesting the people of Bathurst would not understand the implications of their decision.

"A major disadvantage of a popularly-elected mayor is that if the elected mayor does not get on with the other eight councillors then there is nothing we can do about it," she said.