The payment by National was revealed in Parliament by Prime Minister Jacinda Ardern and Regional Economic Development Minister Shane Jones under questioning from Bridges.
Before Question Time Bridges told reporters that the approval of the $350,000 as part of the early projects in the $3 billion provincial growth fund over three years was "frankly incompetence".
"You've got a situation where you've got somewhere, somehow – whether officials or ministers – did not make the appropriate checks to make sure taxpayers' money is being spent wisely," he said.
"What this shows is that the Government takes taxpayers' money very, very lightly."
Bridges said the National government had had some awareness of the issues "but frankly we didn't think the economic case for it stacked up."
He later admitted that he had not known about the $45,000 payments which had been authorised by an official but he had been aware that National had not progressed the project.
He said the point he made was still valid because the Government's approval for $350,000 had been made while SFO investigations were ongoing and that showed a weakness in the system.
"Next time it might be for $48 million."
In Parliament, Gerry Brownlee suggested that Ardern could be misleading the House and demanded she show proof.
The Prime Minister's Office have produced documents showing that New Zealand Trade and Enterprise paid $45,000 in two payments to Waste Energy WC Ltd, a company owned by Gerard Gallagher, which has become Renew Energy.
In August last year Gallagher resigned as director but retained 26 per cent shareholding.
Gallagher along with Simon Nikoloff were investigated over conflicts of interest in their role as employees of the Canterbury Earthquake Recovery Commission and a private business they had set up on the side.
A report commissioned by the State Services Commission found a serious conflict of interest to exist and Commissioner Peter Hughes referred the case to the Serious Fraud Office which is still investigating.
Shane Jones said the $350,000 approval had been put on ice and he was awaiting more information from officials.
The maximum officials can approve under the provincial growth fund is $1 million.
Funding of between $1 million and $20 million requires ministerial approval and projects over $20 million require cabinet approval.
The maximum that officials could approve under National's nearest equivalent, the regional growth programme, was $100,000.