We sent two bikes to NZ when we moved there. They took a long time to arrive (which was fine, we were away travelling) – not one week as was suggested above (which I’m sure is possible, but perhaps more expensive).
Our bikes were in bike bags (so the wheels were removed) and then these were put into a crate, along with our other goods, by the shipping company. In hindsight, this meant we had no control over what was on top of them. One of the bikes was fine but the other one suffered a fork being bent inwards. So I would recommend using those spacers that new bikes come with (you can prob ask your LBS for some) and doing what you can to ensure your bike goes at the top of the crate.
I would agree with hels above – consider selling the bike here and buying new in NZ. Bikes are (or at least were) definitely cheaper out there, and when you factor in the cost of shipping just a bike, plus insurance and the cost of travel to the port at the other end to pick it up etc, you might find you can get a better easier deal this way.