Someone is not well informed if they tell you that "the rate is for non dangerous goods and the bike has to be cleaned of fuel and oil".
Any motor vehicle that has an internal combustion engine in it will be considered 'dangerous goods' for the purpose of air freight, regardless of whether it has fuel, oil, and a battery in it, or whether it has just been manufactured, never fueled or oiled, and never driven. The 'dangerous goods' designation derives from what the shipment is (a 'vehicle, flammable liquid powered, UN category 3166'), not from what condition it is in.
I suggest you find a more knowledgable shipper, or, at least have your shipper look up the category above in the IATA DGR book, where they will also find the appropriate packing instructions (description of how it has to be shipped).
Michael - frequent trans-atlantic moto shipper and also a DGR instructor...