Despite disclosing his criminal past to the NZTA, he was issued a new passenger endorsement in May 2010 and was employed as a school bus driver.
However, his past came to light after a member of the public recognised him as a known child sex offender and reported him. He was immediately dismissed.
NZTA spokesman Andy Knackstedt confirmed Cudby had disclosed his past on his application form, making him subject to a "fit and proper person" check, which prohibits those with serious convictions, including sexual crime, from obtaining a passenger endorsement.
In Cudby's case however, "the law was not applied correctly", Mr Knackstedt said.
"This was a case of human error by the individual processing the application. It was a serious breach of the standards which the NZTA expects of our staff charged with processing these applications."
The person who made the error had already left the NZTA before the mistake came to light.
As soon as the NZTA became aware of Cudby's convictions the passenger endorsement was revoked, Mr Knackstedt said.
The NZTA "apologised unreservedly" for the error.
"We are very disappointed that this has occurred. The NZTA takes our responsibilities in this area very seriously. We understand the distress that this will have caused to parents and others in the community."
Mr Knackstedt said they were confident it was an "isolated case of serious human error".
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