This is extracted from the Canadian Firearms website. It deals specifically with Firearms, not Ammunition, but there is a phone number which may be helpful:
Q. Do I need an export permit to take or ship a firearm out of Canada?
If the firearm is being exported to the United States, you only need an export permit if the firearm is prohibited. When the export and import provisions in the Firearms Act and its supporting regulations come into effect, an export permit will also be required for restricted and non-restricted firearms.
An export permit is required for any class of firearm being exported to a country other than the United States.
That may be written in our Canadian law but that has nothing to do with American law. If a Canadian does not get a permit from the US, then you won't be allowed into the country with a firearm.
