Time or money, your choice.
I would think if the bed is complete the best bet would be to leave it that way and go pick it up yourself, if you have the time. You might have trouble getting someone to disassemble it to ship.
However something to consider is the cost to pick it up. In 1981 AAA announced the average cost per mile to drive was 50 cents. That of course considered more than fuel costs. If you don't own or can't borrow a trailer I have see U-Hall to be pretty pricy for car hauler trailers. For only a pickup bed you shouldn't need that big a trailer. It might be cheaper to have it shipped.
Just my rambling thoughts.
