u need a written approval from ur father .. then apply to SAudi Visa . as a resident in Qatar u will be allowed to BAhrain without VISA ...
but it is much better to go by Air . u can rent a car there for 75 QR per day ... better than wasting ur efforts in driving and borders ..

SAudi VISa should be applied in an agebcy called Asatel just after SAna roundabout .

good luck