The cheapest option is to go to the backpacker hostels and ask for ships that take bikes.
I used Stahlratte (google it) and it was very good. 250$ for the bike and 300$ for me
Mind you, these are sailboats so it will be an adventure to get the bike onboard the boat.
If you have a big/expensive bike, then I would fly it since it is not too expensive (550$ for the bike and 200$ for you) and extremely safe, fast, easy and reliable.
If you look at "shipping the bike" in the sidebar to the left you can see other peoples experiences and phone number for air shipping.
The cheapest air freight company should be Girag (or something)
South East Asia, USA, Central and South America and Scandinavia.