A few days ago Saudi Arabia announced that any GCC resident can now apply for a tourism eVisa. Previously you could only apply for an eVisa if you were from specific countries, while everyone else had to go through a more complicated process that included getting bank statements and visiting the embassy.
With the new announcement, there are still some requirements like your passport being valid for 6+ months, your residency valid for 3+ months and your occupation should be listed as eligible, but these are just minor things.
Once you get your visa online, you can choose to fly to Saudi or just drive there. Al Khobar and Bahrain are around 3-4 hours after crossing the border while Riyadh is around 5. If you missed my guide to driving to Saudi check it here, or apply for a Saudi visa by going to visitsaudi.com/visa