When choosing your flight, particularly when travelling with your bike, it is well worth checking the carriers luggage allowance.
Some carriers have a maximum allowance of only 23kg, whilst others have a 30kg allowance.

With excess charges upto $30 per kilo, big savings can be made by selecting the carrier with the biggest allowance and not necessarily the cheapest flight.

Travelling business class, usually offers an increased allowance.
It is also worth scrutinising transit times, if you are not on a direct flight. Time spent at the airport could be time enjoying your adventure.