Water and electricity are provided and subsidised by the government. You get two bills, both of which are issued by the same government authority.
Unsurprisingly, the Electricity and Water Authority (EWA) supplies water and electricity to Bahrain. To sign up for service, you need to take your contact information, mailing address, and CPR (Central Population Register) card to a local office. At the office, you'll have to fill out a few forms and request for your metre to be read by one of their personnel.
Once your account has been opened, you will start receiving monthly bills which can be paid online, by mail, by telephone, at a bank, at a post office, or at an EWA office. As with any property anywhere, you should keep an eye on your utilities metres to make sure that you are not charged too much.
Although you have water in your home, you should not drink from the tap. You may sanitise your water the old-fashioned way (boiling), but for ease and convenience, have bottled water delivered to your home.
There are only a few gas mains in Bahrain. In most cases, you will need to have it delivered if you want to use gas for cooking or heating water.