Hi Yvonne,
I've done it the other way around..meaning from US to Bali. I'm guessing the process of shipping isn't much different i.e. applying for an export-permit here, and import-permit in the US. Registering the bike with the importpermit, getting insurance etcetc..
Then ofcourse shippingcosts, that would be based on size (box) and weight of the bike, and either air or seafreight. Wich one is cheaper would depend on what the end destination of the scoopy (east-coast/westcoast) would be.
However the most cheapest way is to take the bike apart piece by piece and ship it in boxes via insured mail at the postoffice. Then at destination put it back together. But, I have no idea how to register the bike in the US without having the proper paperwork, so maybe this isn't an option from here to the US.
As for a company who can assist you with this, I know 'Crown relocations' to be a internationally known and trusted company. I used their services for other things.