Hi, first of all, I´d advice you to first read this:
www.horizonsunlimited.com/get-ready/shipping-the-bike

The problem with freighting motorcycles (except on a few more frequently-used routes, which this is not), is that there are no services readily available. So each shipment is an individual case, and there are many, many variables at play, affecting transit time and total costs.

That is why people´s experiences (and costs) may vary a lot, even if they have sent bikes using the same method and on the exact same route, they´ve just done it at a different time, have a little bit different crate sizes, and possibly used a different shipper, for example.

But it can be done. And in this case it´ll happen by sea or by air. The distance from US east coast to NZ is very long, so I´d expect seafreight to be considerably cheaper (by air will probably cost you double, or triple). But it´ll take at least a month by sea, whereas by air it only takes a few days. To avoid confusion, note that “shipping” can refer to all shipping methods, not just seafreight.

The ratio is the same on possible delays: if airfreight cannot be loaded on a certain flight (the cargo hold is already full or something), there´s a good chance it will be put on the next one, and there may be several flights per day. But if your bike is in a container on a big freight ship, and the container is scheduled to change vessel at a certain port, and it misses this connection, the delay could easily be weeks. Happened to my bike in Singapore, when I shipped by sea from Australia to Europe, and it arrived 3 weeks later than scheduled. Luckily that was after the end of my trip!

Also note that seaports are built to handle very big units of cargo, and one motorcycle is very small. Getting the bike loaded on the container/ship, and unloaded at the other end can be painfully slow (and rest assured, they won´t change the way a seaport works in order to get your bike transported quicker!)

Also the fact, that seaport infrastructure is made to move huge volumes of cargo, does not fit you well, when you just want to transport 1 motorcycle: the “start cost” is high, even if you only need this big equipment for 5 minutes, and this is why costs at seaports, particularly at the receiving end, have been bitter surprises for many. (Corruption is another reason, and yet again seaports are often the worst places regarding this... but I think sending US to NZ this should not be such a big problem).