If you hitch hike to Bahrein, you should be aware that it is not allowed to cross the border by foot. Exiting KSA and Bahrain VOA application are performed from booths accessible only to cars. Bus passengers do have to go through immigration desk, though.
İf your driver stops on the Saudi side of the island (it happened to me although it is unlikely), you will have to get another ride to cross the border.
Getting rides is super easy, so no need to take a taxi or private car trying to make a fast buck (250-300 SAR) on you. Humps are great places to get rides.