Accepting a job in KSA and will be living in Bahrain with my wife

You need to understand that a full residence permit in Bahrain with CPR can only be gotten one of few ways:

You are sponsored by an employer for whom you work IN BAHRAIN
You buy property above 50,000 BD and sponsor yourself
You set up a company and sponsor yourself

As a Saudi iqama holder, you can get a longer term visa for Bahrain with a "paper" CPR which allows you to settle and live in Bahrain but you won't get a CPR card.  You can check the differences on many threads in this forum.  To get this, you need some documentation from your Saudi employer such as no objection certificate, CR etc and then an agent in Bahrain to do the formalities for you.  There was a recent thread of someone who was going through the process on which I made a few comments as well - look it up.

Here are few threads, you can find XTang's replies in one of them,

https://www.expat.com/forum/viewtopic.php?id=641869https://www.expat.com/forum/viewtopic.php?id=27589https://www.expat.com/forum/viewtopic.php?id=444539

Good luck

T&R

Hello from Germany,
we are in the same situation. I will move with the children in two weeks because school starts end of August. My husband will follow in October. I am worried how we will get our paper CPR... For the moment we will enter with a tourist visa.
Have you sorted our how you will get your papers? Have you any idea if a tourist visa can be extended and if yes where to do that?
My husbands compy is loacted in KSA. Working visa is already issued. They do not give papers for us. But gave the ok that we live in Bahrain.
Car: I will hire for the first month from SIXT.

Kind regards,
Dunia

For visa extensions, you need to go to NPRA (Immigration) offices on Exhibition road where most visas types can be extended by paying a fee.

As I have said before on many many similar threads, for the paper CPR, you MUST have:

Saudi Iqamas for the entire family
Some documents from the Saudi company - most importantly an NOC & copy of CR

If you do not have or won't get the above, there is NO way that you will get a paper CPR.  You are better off going through the other options listed above by me and getting a full CPR / residence visa.