Always depends on what sort of burkha...they are not all the same.
In the north east province of Saudi, i saw women with leather face coverings.
In Al Khobar, the veils were often completely sheer (making you realise just how beautiful some Saudi women are)...
Worked there myself ;-) Hafr Al Batin...yeah, out in the desert, it was more a Saddiqui environment. It was much better (obviously) in the support offices in Khobar, and Riyadh
I left Saudi as quite a heavy drinker to be honest. Never really was before, and that included the RN.
Used to see native Saudis at parties all the time, particularly at Lockheed, and BAC