Why would you not just have your company in Saudi wire transfer your payments direct to your US bank? Trust me, that will be the best way.. It is the biggest pain to open an account at a Saudi bank, and if your work permit expires before you renew it, your bank funds will be frozen till you get it renewed, so if you are at home, and your work permit expired, you will have no access to your funds till your work permit is renewed.
Doing it this way will also keep the TSA from knocking on your door, since 9/11, when they see funds going from a personal account outside the US to your personal US account, it puts up the RED FLAGS!!! But when it tranfers direct from your company to your home account, it looks like a normal business transfer.
I would say, open an account there, and keep just a small amount in it, plus, banks there will not exchange US dollars without you having an account anyways.