Trucks are 8 feet wide and 40 feet long, more or less. Some are a bit longer, there are 53 foot trailers.
When you ship, you pay both for weight, and for length of bed taken up.

So even if something is light, relatively speaking, if it has to lay flat, and its 8 feet wide and 11 feet long, you pay for 11 feet of truck bed.

I use freight brokers to ship oddball stuff like this- look in your local yellow pages, or ask at a nearby truck stop.
A freight broker will find you an independent trucker, and thats the best way for art. I tend to use flatbeds, as its easier to load and unload, but there are fewer flatbeds out there than box trailers. Depends on weight, and situation at each end.

If it was me, I would probably plastic wrap it, with a 2' wide roll of saran wrap they use for wrapping pallets, then block it up on 4"x4" dunnage.
But I would sit it flat on the bed, and make sure nothing else got put on top of it.

When you use a flatbed without crating or wrapping, stuff can get dirty. You can get truckers to tarp it for you, but that costs extra- more than you would think, as truck tarps are expensive, and dont last all that long flapping in the wind at 70mph.

I never use common carriers, like Yellow Freight or Roadway for stuff like this. They will transfer it 4 or 5 times from truck to terminal to truck, and they WILL dent and damage it, unless its completely crated, and even then they will try their best. Plus, they are always more expensive than a freight broker/independent combo.

prices vary a lot, depending on what diesel costs this month, who is going where, and where you live. I can imagine this costing anywhere from $500 to a bit over a grand to ship, assuming you lay it flat and it takes up a full 11 feet of bed.

I like to load it myself, make sure that it will stay on the same truck direct to its destination, and then I often fly down and unload and install.

I guess we all have our preferences ...personally I like to keep grillwork vertical and strapped to the side of a box.We will often strap a pallet or two to the exposed surface just in case something lumpy gets loaded next to the metal.Usually costs less this way too....
Moving grills down the inside of a container or truck is easier vertical because you can roll it on a piano pallet or tubes.
One thing to bear in mind when getting a quote is to avoid the word "art". Prices seem to jump. Architectural metalwork is more common place.
good luck
Giusseppe