The victim was pronounced dead at the scene of the crash at Main and Mary streets shortly before 2 p.m.
The bus was part of Route No. 72, which runs between Newark and Paterson, officials said.
There were no summonses immediately issued to the driver of the #72 NJ Transit bus, which runs between Newark and Paterson.
Nor were there any immediate indications that the driver did anything wrong, Passaic County Prosecutor Camelia M. Valdes and Paterson Police Chief Troy Oswald said in a joint release.
An investigation was continuing, they said.
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