Having just sent a bow to Romania I can give you the ins and outs of what I did that seemed to work very well.
As far as funds transfer, have the money wired with Western Union. No account required, just the transfer number, photo ID, and who the money was coming from. Once transferred, the funds are available for immediate pick up. Many grocery stores are Western Union offices so you may be able to pick up the cash at the local food store.
For shipping, USPS was the way to go. All of the other shipping companies wanted an arm and a leg for shipping costs (>$250) as opposed to (~$45) for USPS. Shipping time to Romania was set at 7-10 days (+ customs). You will have to fill out a customs declaration form at the post office (no big deal).
If you are sending a bow, you may be better off taking the limbs off it and sending it in a much smaller box. If you go over the size limit (I believe it is 41") then you have to use priority shipping which pushes the cost up several hundred dollars. I also think that a bow with the limbs off, packed in a smaller box has a better chance of survival than one that is strung.