Bahrain has three main mobile operators — Batelco, stc Bahrain, and Zain Bahrain. You can buy a prepaid SIM within minutes at any operator shop, at the airport on arrival, or in most malls; bring your passport (and your CPR once you have it), since SIMs must be registered to an ID.
If you are here for a short stay, you may not need a physical SIM at all. Batelco and stc both publish eSIM options, so an eSIM-capable phone can get connected without queueing in a shop — Batelco advertises activating a prepaid or postpaid line from its app with a selfie and an ID scan, though the line can only be activated once you are physically in Bahrain, and switching back to a physical SIM later carries a fee. Zain's published eSIM page was not reachable when we checked, so confirm availability with them directly if they are your preferred network.
For a longer stay, all three sell home internet over 5G or fibre alongside their mobile plans. Bundles and pricing change often, so compare current offers in-store or on the operators' own sites before committing to a postpaid contract.