Saudi registered car how long to stay in Bahrain or

The problem is not the car.  You can keep it here.  What needs to be considered is:

1) Does insurance cover damages for another driver and outside of KSA?

2) Third party insurance from causeway needs to be valid for the duration because if there is an accident and there is no third party, you will be personally liable

3) Insurance and registration will have to be renewed in Saudi periodically so car has to go back and forth a few times

@XTang thank you for your reply as always.

Does it matter that the owner of the car, driving it into Bahrain (my husband) is not the person that will be driving it in Bahrain (me)?

What I mean is, he will leave me the car and fly back to KSA.

Could this be an issue??

Not inside Bahrain, no.   But check insurance because I know many people in similar situation to you who had an accident and then paid a lot of money out of their own pocket.  One had to pay a massive amount on account of third party liability as their causeway insurance was even expired.