Hi, my wife and I bought tickets from Santiago to Aukland from LAN for about US$1200 each. The bike goes via sea freight for about the same price.
Ask any LAN office about their current special rates. We used the office in Valparaiso. If you dont ask for their special, they quote normal prices. We bought these tickets two months ago, so maybe we were better of buying it in advance.
Hope you get a good deal, prices in general are rediculous and expensive.