Yes, I went out to work in Admin for an oil company. As a single female we had to live on camp. The (Saudi) company had various compounds and ours was one of the smallest. It had beautiful white sandy beach fringed with palm trees, a ladies and a mens gym, squash courts, tennis courts, bowling alley, cinema, library, supermarket, florist, stables, running track, football pitches, baseball pitches, various coffee shops, restaurants, supermarket, golf club, golf course, yacht club. Then there were self directed groups.
They do the chopping usually on a Friday after they go to the mosque. I made sure I never saw anything like that. It would be reported in the Arab news the next day or two later.
Did you ever see the film, "The Kingdom?"
I could wear conservative clothes on camp and when I went off camp too. When 9/11 happened the atmosphere changed. From then on I always wore the black cloak called an abaya. I was in the Easter Province which is more easy going (but not much) and so would not cover my hair unless I was shouted at.
Once off camp you got taxis everywhere if you didn't have a man to drive you.
Bahrain is connected to Saudi by a bridge and that would be the favourite place to go if you had time. Bahrain is very tolerant and you can get pork and alcohol there and women drive.
It is quite an indulgent life for western expats.
Thank you for asking.