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1) You won't be able to go into Bahrain unless or until you have a visa.  The causeway is closed for normal traffic but they let Bahrain citizens, residents or visa holders exit Saudi one-way and are only letting Saudi citizens back in
2) Forget about taxi service, no one will take you across causeway as for one, they won't be allowed to enter Bahrain (or exit Saudi) and also °µÍø½ûÇø drivers won't be able to come back into Saudi.  You will have to go in your own car

Your best bet is to find any repatriation flight out of Saudi and then connect from there to Bahrain.  Ship your stuff via air cargo.

Or if you have connections, use them to smooth your way across the causeway.

appreciate the quick response, Yes I have a visa, Khobar the taxis are driven by Saudis? arent they able to go back and forth to Bahrain. I thought that the causeway was open for individuals. I also just checked that regular flights from Riyadh to Bahrain are available online and gulf air app as well, or is it possible for me to rent a car and drive to Bahrain are there any car rentals providing this service in Khobar

I don't think you follow the news.

1) All scheduled international commercial flights from Saudi are suspended since March and till today. Just because you see it online doesn't mean the flight is operating.  They have been putting it on their websites since April and it keeps getting cancelled.   Go and see the flight status for the flights you are referring to, for the past days.  Very few flights are operating as repatriation flights which you need to book through the Awdah app.  There are some others to European destinations which are semi regular (one-way tickets can be purchased on these)

2) No, the causeway is NOT open for back and forth travel - officially it is closed since March.  They have only allowed exceptions for following categories:

Commercial trucks
Saudi citizens who want to come back to Saudi from Bahrain
Bahrain citizens/residents/visa holders who want to exit Saudi

And to answer your other query, Saudi immigration won't let a Saudi citizen exit unless he can really convince them i.e. that he has family or whatever.....which a taxi driver won't be able to.  And till today, whoever enters Bahrain won't be able to turn around and go back as there is a mandatory 10 day quarantine. 

That is why I said, unless the situation changes or you have connections, make another plan.

or is it possible for me to rent a car and drive to Bahrain are there any car rentals providing this service in Khobar

You can rent a car, it just costs extra to take it across border plus permission from that agency. But that car will be stuck in Bahrain so don't know if any agency will agree to that.  Maybe if you pay a lot to get that car shipped back by truck... Dunno.  You have to ask different agencies.

can you recommend some agencies which I can contact for car rental, or if I take my own car to bahrain can I ship it back to KSA? what documents would I require for that (if it works)?

You can drive your car and ship it back.

If you want to keep it in Bahrain then that's an export process and there are many threads in the forum about that. Use search in Bahrain forums.

Agencies just Google and start calling them.

Thanks, Xtang for all the help full replies really appreciate it.