LEGALLY you can not throw it into a USPS box!
So, you must ship it ground UPS or Fedex, you are required to have a tag / sticker thingy put on it, stating it is ammunition, a form of hazardous material. It does not cost extra, but ammo is just heavy.
I have shipped a box for around $5 or $6 buckeroos, a larger amount is cheaper (perse', as UPS ships in volume), so 4 or 5 boxes is less than $20 to ship.
I traded a guy a bunch of 5.56 for WW2 45 ACP, we just shipped it UPS to each other.
Ed