The bus is finally due in Auckland at 12.30pm "barring further incident" - more than six and a half hours after it was due at 5.50am.
Passenger Jonah Park, a postgraduate law student at Auckland University, said many passengers were workers who would be late to work today.
"There are mechanics and nurses and a lot of other people," he said.
"Quite a few passengers have been sending emails overnight but there has been no contact, no replies. Naked Bus as a company isn't taking care of the situation at all.
"Many of us here are saying we won't travel Naked Bus again. Mechanical failures and things like that are one thing, but having no respect for passengers, that's kind of appalling."
Naked Bus owner Hamish Nuttall told the Herald the company was now contacting all passengers to apologise and offer them a full refund plus a free trip in the future.
"Last night, the overnight service from Wellington to Auckland had a mechanical failure which meant that the bus had to be replaced. As it was at night, it took some time to find a replacement vehicle which had to be sourced from Palmerston North," he said.
"Unfortunately the replacement vehicle then suffered a flat tyre. This delayed the service further.
"Naked Bus takes reliability extremely seriously. We have a preventive maintenance programme in place, and we monitor all mechanical issues. It is extremely unfortunate that one service suffered two unconnected but serious issues.
"We would also like to thank the driver, who has been complimented on his handling of the situation by passengers."
The cut-rate bus company, founded by Mr Nuttall in 2006, has had a succession of problems. A driver was sacked last year after allegedly refusing to stop to let a young woman go to the toilet, forcing her to urinate on the bus. In April another Wellington to Auckland bus ran out of fuel in Cambridge because the driver had slept in that morning.
Mr Park said he paid the full price of $20.50 for his ticket last night. Although some others had paid as little as $12, he said the series of mishaps had been costly in lost working hours and other costs.
"A lot of us had to buy coffee and eat meals and things like that just to keep ourselves warm," he said.
"Having said that, there are some real cool people on the bus. The driver was not at fault."
