The cash would be split over two payments, with half given if the deal's agreed to and the rest in December.
NZ Bus will also keep the provision of five weeks' annual leave for all existing staff, and increase the base hourly rate for drivers with at least six months' experience to $24 per hour.
Chief Operating Officer Jay Zmijewski said they had listened to the union's concerns and believed the offer was good for both existing and new drivers.
"The proposed deal takes the base rate for our drivers to well above the living wage of $22.10. The rate of $24 per hour that NZ Bus is offering is an increase to the base wage of up to 24.4 per cent.
"We have consistently said that we want to pay our drivers more and this deal delivers on that. This deal ensures our drivers continue to enjoy the best pay and the best conditions of any operator in the NZ bus industry."
The union is holding a stopwork meeting on Thursday to consider the new deal, however Tramways Union secretary Kevin O'Sullivan has already expressed his disappointment.
He said the extra money comes at the cost of drivers' benefits, like being paid overtime, and they are opposed to selling conditions for cash.
Off-peak bus services will be cancelled between 9am and 3pm during Thursday's meeting.