The Western Bay's council, however, has submitted against the bill, with mayor Garry Webber saying the system would be costly to administer and might result in inconsistent funding decisions.
"We also have concerns at how the scheme may lead to a level of inequity between regions, with fuel taxes between nominal boundaries varying and encouraging unnecessary trips to take advantage of cheaper fuel available."
The bill would allow Auckland to establish a fuel tax by July 1 and for other areas in New Zealand to introduce their own fuel taxes from 2021.
Auckland's council has strongly supported an 11.5c per litre fuel tax for the supercity.
Consultation is underway with Auckland Council set to formally approve the tax on May 31, allowing it would come into effect on July 1.
Revenue from the fuel tax will go to the local regional council to fund local transport projects.
Brownless said in the letter that the Bay of Plenty was expected to spend $2.338 billion over the next seven years on transport projects eligible for central Government funding.
"Over the same period, a further $115 million land transport expenditure has been identified that is not eligible for funding support from the NLTF. The availability of a fuel tax would provide a potential revenue source to fund those activities.
"Given the funding pressures on growth councils, we request that regions outside of
Auckland are allowed to implement a fuel tax earlier than 2021."
Bridges, who as opposition leader has said National would overturn the regional fuel tax legislation if returned to Government in 2020, said Tauranga did not need a fuel tax.
"The fuel tax won't make a blind bit of difference to the transport issues Tauranga has," Bridges said.
"Some experts say petrol prices might hit $3 per litre - the Government shouldn't help that along."
He accused the coalition Government of taking money away from regional roads and putting it "into a single tram in Auckland".
"The Government is awash with cash as a result of the strong economy over the last few years ... but the priorities are all wrong."
In a meeting at 1.30pm, Tauranga City Council's transport committee will be asked to retrospectively approve the council's submission - dated April 17 - to the bill.