The shuttle from the cruise ship took us to Lyttleton city in about 5 mins. (maps below), where we took a shuttle to christchurch (I believe it was under 2$ and 35 mins ride) to bus station in Christchurch)
https://www.google.com/maps/dir/Lyttelton,+New+Zealand/Christchurch,+New+Zealand/@-43.6029903,172.7179308,18.19z/data=!4m14!4m13!1m5!1m1!1s0x6d32262b7f7377c1:0x500ef86847985c0!2m2!1d172.7169812!2d-43.6027462!1m5!1m1!1s0x6d322f4863c5ed01:0x500ef8684799945!2m2!1d172.6305589!2d-43.5320214!5i2?entry=ttu