Few people have drivers.
Depending on how senior your position is you might be able to get your employer to provide one although the norm is for you to hire a driver for a monthly salary of 1000-1500 Riyals.

Just take the plunge. Once you've learned the basics of local traffic chaos you'll be ok.
A major contributing factor is the diversity of nationalities taking hold of cars and driving them as they would back home.

Watch out for the (new) taxis, Land Cruisers and the occasional Mitsubishi Magna VRX whose drivers seem to think they're piloting an F-16 due to the presence of one large and utterly useless wing on the boot/trunk.

Also kids with caps barely visible above the steering wheel are a sure sign of trouble.