Does the seller have an export permit? Is the modern or pre 1898? What is the value of the gun? Lot of variables to consider. You can do a search here and find old post that coever the issues.
As a general rule if you are paying someone to handle both ends and all the shipping will set you back 500-750. It will go up from there if you need extra insurance or have import duties to pay. Some will do it for a little less and some for a lot more. You get what you pay for. If someone is shipping several other guns at the same time you may get a slightly better deal. It can be a lot of time and work for one gun. More so if you are dealing with govt. people who do not know what to do and act like you are dumber than they are. A small miracle in most cases.
Best bet is to have someone who does it on a regular basis do it for you. SKB would be my bet at
http://www.bertramandco.com .