An ESD is nothing more then a pet, and most trucking companies DO NOT allow pets in their trucks. Your dog is not considered a service dog, it is a pet.
Are you talking about Swift Transportation, the trucking company? If so, I did a little research. It looks like you can bring a dog with you for any reason you may have, but you have to put down a deposit. I'm guessing it's to ensure that no damage will come to the cab because of your dog, and if nothing happens the deposit will be refunded. I hope this is what you were talking about, and I hope my answer helps!
Who or what is swift?