Try James Cargo. They are specialists in motorcycle transportation and will do everything for you if you want; documentation, pick the bike up, take it to Heathrow, crate it up etc. You can save a bit by crating it yourself and delivering it to them at the airport. Costs about a grand (or did) if I recall, but you bike could be in the US the next day if you get the logistics right.

I haven't used them personally, but several people I know have over the years, including my dad, who transported his BMW there 2006 for 3 months.

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