You do drive through the actual zoo. You show your ticket at the parking lot, then head out of the lot and up the hill. You enter via the gate just at the top by the elevators. From there you drive through the zoo. It follows the main path all the way until you reach the path which turns down the hill back towards the tiger enclosure and entrance, where you exit out another gate onto the road.

You never need to leave the car and it is about 30-45 minutes depending on how fast the cars in front of you are going.

The price is per vehicle, not per passenger, so if you have friends you would want to go with, then you can split the cost.