Have you tried contacting one of the international airlines that are based in Iceland and asking them if they would be interested in shipping your bike on a 'space available' basis?
If you are planning to ship during a time period that is low or shoulder season for air travel, then you could get a very good deal from the airline. If they have aircraft going out with less than a full loads by weight and cube, then they would probably be happy to pick up US$ 1,000 or perhaps even less for taking your bike. This is a whole heck of a lot less money than 'positive space' air freight would cost you.
A used motorcycle is considered 'dangerous goods' so far as IATA is concerned - UN number 3166, which is "Vehicle, flammable liquid powered" but generally all you have to do is comply with IATA packing instruction 900, which you can get details of from any airline cargo office. Usually, this means you show up with less than a gallon of gas, and disconnect the battery.
Two airlines you might want to contact are Icelandair and Atlantica. I'm sorry I don't have contact info or URL's for either of them. If your motorcycle is large, you will probably be restricted to a widebody aircraft that can accept a LD6 container.