Visit dating websites in the Resources section of this article. Register your profile to be able to browse through female profiles of the other registered members. Mind, however, that some of the profiles look suspicious and could have been submitted by escort agencies (illegal in Saudi Arabia).
Ask your friends and relatives in Jeddah whether they know an unmarried woman whom you could date. Local customs are very strict about dating. For example, women are generally not allowed to date men without consent of their fathers. Dating a woman without an intention to marry her is also considered immoral in the kingdom.
Ask your colleagues to help you attend expatriate parties in Jeddah. While dating a local woman is a challenge, having a relationship with a female expat from a Western country is somewhat easier. Still, because most of the expatriates working in Saudi Arabia are men, the competition is rather elevated.