Check uship.com. You enter your info, i.e. what you're shipping, from where to where, you can enter a budget but not necessary. It goes out to haulers/transporters who subscribe to this service. I posted a job to haul two horse from Indiana to South Dakota about 10 days ago. Got one bidder, emailed back and forth a few times to feel them out, and accepted the bid. He's picking them up in the morning, hauling to Kansas to lay over night at his ranch, and delivering them near Rapid City Thursday.
He's an equine dentist that travels the country to work on horses and transports about anything he can pick up to help with expenses and some extra money. Since he's traveling anyway, he just as well make something while he's doing it. Once we started emailing, I checked to see if he had a website, and found his facebook page. That helped put me at ease that he was on the up and up.