You won't be able to pack your bicycle into a suitcase within the size limit unless you've got a folding bicycle.
Look at the link the first poster posted ... and then look up the airline regulations with regard to bicycles. Then choose an airline that doesn't charge very much. I think Qantas flies to Bali ... they don't charge for bicycles. If Air Canada flies to Bali (not sure if they do), they'd only charge you $50. Do your research.
And when you get to the airport, arrive very early, be the first person in line, and be as friendly, helpful, pleasant, nice, and cheerful as possible. Sometimes it helps.