From August 21, Stop B on Willow St will be relocated around the corner to Wharf St, and the regional bus stop Stop D will be moved further up Wharf St.
Library book drop-off is at the main entrance to the library, which can be accessed from Wharf or Willow streets.
The council's Customer Service Centre and the library will be open normal hours.
Mobility parking in the library car park has been relocated, with two additional mobility spaces added in Masonic Park and one on Durham St near Baycourt.
The council apologises for any inconvenience during this time and appreciates understanding while work is underway.
Once demolition work is complete at Willow St, Little Big Events will be activating the space for the community, the council said.
"This will be in place until investment decisions are made on the future of the space and the site is developed."
As part of the Civic Heart Long Term Plan amendment in September 2016, the council resolved to demolish the administration building as soon as practically possible after finding toxic mould in the building in November 2014.