The best way to transfer ownership while abroad
Well for German bikes transfer of ownership is just handling over the paper "KFZ Brief bzw Zulassungsbescheinigung Teil 2) and writing a contract and paying. If the bike is financed and bank owned, the "cool" rider should not have this document (typical for BMW riders HAHA).
No Notaria needed as in Chile. One could legally do so at a boarder between two country's...export the bike from the old owners passport and import it on the new owners passport. (Importing bikes with other names in the papers without a little bribe is not possible in every country.) Therefor he might need a more common power of authority document too just to make shure if some stupid officials don't accept the "Kaufvertrag".
Only problem for the old owner he keeps on paying tax and insurance for the bike until the new owner unregisters the bike so the old owner should unregister the bike once he leaves the EU or should do so at an embassy. Cant be so different from UK bikes...EU procedures should be all the same...