His party would instead fund new infrastructure through the national budget.
"A National government under me will invest heavily in transport … but we won't be using a regional fuel tax to do so.
"If we manage the books right, we don't need it."
He said the previous National Government was able to invest in major infrastructure like the Waterview tunnel while still "living within our means".
Transport Minister Phil Twyford said Bridges' transport plan would keep Auckland "in the dark ages".
"Aucklanders want their traffic nightmare to end now," he said.
"The majority of Aucklanders want a regional fuel tax because they understand the rest of the country cannot fund their transport solutions."
Regional fuel taxes would raise $4.3 billion, and Bridges would need to cut social services or infrastructure if he was going to scrap the measure, he said.
That would include cutting Auckland transport projects like Mill Road or Penlink, which the tax would pay for.
In his speech, Bridges also targeted the Provincial Growth Fund, saying it was "terrible policy". It would shift businesses' focus away from being more productive to "chasing a subsidy from Matua Shane", he said.
"When I was Economic Development Minister, our plan for the economy was set out in the Business Growth Agenda.
"The BGA comprised over 500 different initiatives all designed to make it easier to do business by investing in infrastructure, removing red tape, and helping Kiwis develop the skills needed in a modern economy.
"Some of those were big, some were small. I'll admit some weren't as exciting spending a billion dollars every year. But together they were effective."
One of the themes of the speech was that the Labour-NZ First-Greens coalition was becoming increasingly interventionist.
Government had a role to play in encouraging business, he said, but it should "get the settings right and then get out of the way".
He cited the Labour coalition's ban on offshore new oil and gas exploration, saying the Government had prematurely predicted that there would be no job losses.
"On that day I happened to be in New Plymouth at a company called Fitzroy Engineering, which employs around 400 people.
"Within hours the CEO had said there would be no more investment and no more hiring.
"He knows the impact on his business better than the politicians in Wellington."
Bridges - who will speak at a public meeting in oil-rich Taranaki later today - reiterated that a National-led Government would begin exploring for oil and gas again.
"It is one thing to do something because it makes a nice headline, but the reality is the impact on the thousands of people who have their jobs taken away will last a lifetime."
