Hi, sorry to take so long to answer but I lost the info I wanted to pass on to you.
Contact Dave Milligan at his company called Get Routed. They ship bikes on a regular basis to NZ. Mostly from Melbourne but he also does some shipments out of Sydney as well I am lead to believe. He books the whole container so it is a group or individual type arrangement.
Sydney is the dearest port to deal with in this country when it comes to port fees, customs etc. Not sure the Melbourne is that much cheaper. They use official names for their charges rather than calling them bribes in Australia. And they do the same to us locals as well, so dont think the high charges are just for your benefit.
The web site to look up is
Good Luck, Cheryl.