Gollygee- if there were one simple regulation on this, would be a piece of cake. Unfortunately, anything but simple.
The "regulation" is a combination of 19 CFR 142 (Federal Dept of Transportation reg on Hazardous Materials transport) the US Domestic Mail Manual (regs for US Post Office) and the tariffs of UPS and FedEx.
Here it is in a nutshell-
You cannot mail ammunition by US Mail. Period. Brass or bullets, sure. People that get cute with US Mail get to meet US Postal Inspection Service- the folks that have the highest conviction rate of any Federal Law Enforcement agency.
Loaded ordinary ammunition in quantities of 66 lbs or less may be shipped by UPS or FedEx in GROUND shipment only (there is an exception to the GROUND part for Alaska- lack of roads, y'know). The local UPS store may refuse to accept the shipment- those are franchises, not run by UPS. Take it to a UPS Hub, or schedule a pickup.
Smokeless powder, black powder, BP substitute, primers and percussion caps CAN be shipped UPS ground (hell, they even deliver blasting caps) HOWEVER- those items fall into a different shipping classification than ammo. Those items, and large amounts of ammo- or ammo other than "ordinary" rifle, shotgun, or handgun ammo- such as tracer, incendiary, tear gas, etc- gets bumped into the HAZMAT shipping category.
The actual term for regular ammo is "Cartridges, Small Arms". The package carries a shipping label that looks like this:
The reason that AMMO can be shipped but powder/primers is shipped as HAZMAT- is the hazard of mass detonation. When assembled into cartridges, the brass and bullets provides mass that will absorb energy of a cartridge that should fire- and the whole box does not go off. However, if one primer in a box fires, they ALL may fire.
You can verify this by calling UPS Services, but do so when you have plenty of time to be on hold.
Summary- Never mail ammo. Ship ammo UPS GROUND, 66 lbs or less, use the ORM-D label.