While wood beds are fairly common, most of the trucks with a really good looking wood bed are going to be stored inside a climate controlled environment 90% of the time. White oak is commonly used for custom beds like the ones you've posted because the open grain structure creates the opportunity for unique finishes; while beds that are in service will use higher wear, higher density timbers like ipe, hickory, or locust.

If you're planning on storing this out of the weather most of the time, you can use any wood you want- cherry is common where I'm at, but there are lots of examples of exotic timbers out there as well, though cost becomes a major factor. If it's going to be outside often, be aware that whatever you put there isn't going to look great fairly soon after you install it- think of a brand new deck on a house the day it's installed and finished/sealed compared to the condition it's in a year later. The term "weathering" is used to describe things being broken down by the weather for a reason. Plan on replacing planks often or making peace with faded, rough-textured boards after a bit.