By train
By train
Dammam's train station is 15 min away by taxi.
By bus
By bus
The Saudi-Bahraini Transport Company SABTCO (http://www.sabtco.biz/) has five buses daily to Bahrain, see that article for details. The SABTCO office is in the center of the city, just ask any taxi driver.
The nearest main bus station is in Dammam, but SAPTCO (http://www.saptco.com.sa/) also offers direct VIP services from Riyadh to Khobar.