foam packaging and any normal carrier like Fedex or UPS.
A box is usually not reasonable for something like this. Instead buy foam wrapping, It has soft foam that is kinda thick, but still flexible, and is a tarp-like material on the opposite side. Wrap the bumper in this material multiple times around to give it a nice cushion.
Use packing tape to bind the seams together, and fold the ends like a burrito. Once you're done you can label it and send it on it's way!
Oh and I forgot to say, it can be pretty pricey in terms of shipping., not because of weight, because it is usually light. But because of irregular shape/size.