Driving rating will increase as you:
- Kill enemies by running them over
- Beat Road Races (see "Road Warrior")
- Jump through Stunt Markers (see "Ring Leader")
- Do stunts (see "Stunt Driver")
- Collect Hidden Orbs (see "Orb Hunter")
The quickest way to get your Driving rating up is to kill enemies by running them over. The easiest way to run enemies over is to find an area full of them and fishtail by holding Reverse and Left or Right at the same time. The best place I have found to do this is the area around Los Muertos boss Violetta Sanchez before eliminating her. Just circle the building she is in or go through the court yard and run over any gang member you see. If you focus solely on this, you can max your rating in about an hour and a half or less, depending on your skill. Driving slower makes it easier as the gang members are less likely to move out of the way.
Note: Killing civilians or peacekeepers by running them over will decrease your rating.