Unfortunately, even cargo airlines are getting a bit difficult about flying motorcycles if you've not done business with them before.
A few thoughts:
If you can send the bike in advance by sea, you might be interested in these:
1. A company mentioned by Erin & Chris Ratay for shipping from LA to Dunedin. Cost quoted was US$270 per bike, which sounds a lot better than $2,000. We usually don't recommend sea shipments, but NZ isn't in the same category as Africa.
2. Another possibility is Direct Express, a company in Gardena, California which specialises in car-shipment, per Peter Theuwissen. He shipped his bike to Australia for US$450 in March 2000, but they don't have a website so cannot tell whether they ship to NZ. You'll have to call them directly. Contact details are on the Shipping page:
3. Finally, we have recently learned of California Shipping, a company "specializing in the export/containerizing of autos, trailerized boats, motorcycles, auto-parts and accompanying cargo to the major ports of Europe, Scandinavia, Australia and New Zealand". http://www.calship.com/
With sea shipments, you need to allow at least 8-10 weeks for the bike to get to NZ, though.
Depending on how long you plan to stay in NZ, you might consider buying a bike there and selling at the end of your trip, rather than pay for shipment in both directions.
Let us know how you make out.
Good luck and safe travels!
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