How to visit Saudi as a resident of Bahrain

Hello everyone,

I hope you are all having a beautiful day in Bahrain. We would like to visit Saudi for the day with the kids, and take them to a zoo that I've heard about. The problem is that we are American citizens with Bahrain Residency Visas and I'm not sure what is required for this adventure.

I have called the Saudi embassy several times over the course of the last two weeks and can not get an answer. I don't have the vehicular access necessary to ask them in person, so I was hoping maybe one of you might know?

I have heard rumors that we can go through the gate with only our CPR cards. I'm not so sure about that though,  because I've also heard rumors that they don't give visas to practically anyone. Which may not be relevant if we really don't need a visa to get over, but I'm sure one of you can help me find the reality.

Thanks for the help. Have a wonderful week.