Four young men handed themselves in to police over the theft of the cash box.
A 17-year-old and a 20-year-old were charged by police with the theft, while two other teenagers - aged 15 and 16 - were referred to Youth Aid.
Wellington buses will run to normal timetable until 9am on Monday, and will continue as normal after 2pm.
Meanwhile, a GO Wellington shuttle service from Wellington Airport to Queensgate will operate between 9.30am and 2pm.
School bus services, GO Wellington and Runciman's services are not affected, the company says.
A spokesperson said: "We apologise for any inconvenience and trust that our customers will make alternative travel arrangements."