According to the USDA, as long as the ants are shipped from a coastal state and do not require interstate transported before leaving the country, their office would not require any sort of permit.
I assume if you want to move them interstate you would need to apply for a 526 permit or something similar. I live in Florida so I haven't looked into it.
The FWS would require a standard commercial wild life export license (one time fee of $100) and each shipment would need to be declared, shipped from a specific port, and inspected by a customs officer, the inspection fee would be $186 for each shipment.
Tl;dr legal exportation from the U.S. is easy but costs $200-300 in export fees
Edited by SuperFrank, August 9 2020 - 1:09 AM.