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I am confused on the first part.

You cannot exit Saudi on an Iqama without an exit re-entry visa to begin with.  The fact that you were already travelling to Bahrain on your Iqama before implies that you DID HAVE an ERE to begin with.  Maybe now you got a multiple ERE vs. the single ERE you had before?

Putting that aside, the Bahrain visa type does not matter.   The process is the same.  Unless you are entering Bahrain for the first time on that employment visa (i.e. you got a visa but it hasn't been converted to a residence permit), in which case they will ask you to park your car and go into a room for biometrics and a photo.

You can take your car if it is under your name.  If it is under the bank's name or an employer's name, you will need their approval to take it out of Saudi.  If you don't have that approval, Saudi customs, where you get the slip, will turn you back.

Thanks for such valuable advice. Yes, I am currently holding multiple exit re-entry, and my IQAMA is still valid. So, as I understand from your response, I can go through Causeway. ( So I am not booking flight tickets.) I can enter an employment visa, and in the next 8-10 days, I will get a valid CPR from them and be back. Yes, the car is also under my name.  Thanks for such gentle advice.