I shipped a bike frame to Australia a few years back. I used bikeflights.com. If you buy through them it's a discounted price on Fedex shipping (at least it was back then). I don't recall the exact price of shipping as the buyer bought the shipping and sent me the shipping label. It got there in a week and the buyer was happy. (It was an expensive carbon fiber frame.)

So you could buy the shipping label and send it to your bikeshop and they can ship the box.