Not that it helps you, but it is great with Air New Zealand, they let you take bikes for free, and are lovely about it.
The customs stuff, clean it with a toothbrush until there is not a speck of dirt on it, especially on the tyres. Then clean it a bit more. Then bag it. They will still spray it, but if it looks like you have made an effort to clean it yourself, they won't charge you for doing it (and I hear the charges can be quite big).
The second time I took a bike into NZ, I did this, and it was dead easy. The first time, I had it pretty clean, but not perfect, and I had to do the whole sorry I'm a stupid foreigner act in order to avoid paying out money. Whatever you do, don't get angry with the customs people – if you are lovely and friendly and slightly confused, they will be much more likely to help you out than if you are a grump. Expect it to add about 30-40 minutes to the time you take getting out of the airport.
Joe