I believe you must mark the package with an "ORD" diamond ordnance label, but loaded ammo doesn't have to be shipped as HAZMAT.
UPS, FedEx, DHL and other commercial shippers are your options.
As David mentions above, reloading components like powder and primers do have to ship as HAZMAT.
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 Igitur si vis pacem, para bellum -
- Therefore if you want peace, prepare for war.
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