You can ship it UPS as long as it is properly labeled as ORM-D. From their FAQ:
And from their "Learn more about shipping firearms, handguns and ammunition" linkQ
Can we ship ammunition through UPS? If so, what steps are required?
Ammunition must be shipped separately from packages that contain firearms. Only ammunition suitable for .50-caliber firearms or smaller is allowed. Also, when shipping, it’s important to print “ORM-D” on the package. Ammunition can be shipped only within the 48 contiguous states. Learn more about shipping firearms, handguns and ammunition.
Finally, here's a link that discusses the topic and shows the new labeling required:Ammunition must be shipped separately from packages that contain firearms (including handguns).
Ammunition will be transported only when packaged and labeled in compliance with 49 C.F.R. § 172 regarding hazardous materials shipments, and must be shipped in accordance with the UPS Guide for Shipping Ground and Air Hazardous Materials.