All embassies usually throw parties at least once a month.
You can then do a global search for people in your area and message away.
Warning: It is very unusual for a Saudi not be married past the late 20s.
Ok, I kid, but Saudi men can get very possessive and jealous.
A second thing I need to point out is tribal thinking.
The punishment for sex outside of marriage is a hefty number of lashes.
Do not–absolutely do not–date a married woman (and some may try to approach you). Saudi Arabia has one of the highest worldwide ratios of twitter and facebook users when compared to population.
Secondly, Saudi girls usually walk around in groups. You must remain very close when in the store, they can’t be seen approaching you.
The important thing here is how you look (your clothes), eye contact, and the lead away from open public areas.
A lot of this is attributed to the strict social life, so you’ll find many people meet online.