In The Big Bang Theory S09E19, "The Solder Excursion Diversion" episode, we come to know that Sheldon deposits every single piece of his used belongings in the Storage vault, and he says that Amy is the one and only other person who knows about this.
The question is who could have helped him in moving all the other stuff because he needs someone to drive him over there.
Well my guess is that he would have used a cab or a bus for such occasions. Although this is true that due to reasons such as being over sensitive about hygiene and security and being "too evolved for driving", he almost always gets around by making other people to drive him over to places, but in this case it is logical to assume that he would have made an exception to his usual and preferred conveyance arrangements as he needed to hide this place from everybody else. He called his storage unit his "Fortress of Shame". And hence would have made other arrangements like a cab or a bus to take his used stuff there.