Verizon phones don't have that menu setup:
Settings/Application manager/ scroll over to the right to "Turned Off"
In "All" I can see 'Car Mode' but it does not have the option to do anything except "Force Stop"
It does NOT show up anywhere in the Menu system, or in the Apps Grid menus.
I doubled checked for "hidden" and "disabled". Not there either.
I switched to Easy Mode, but is that totally useless and destroyed all of my screens. Lasted about 3 seconds, switched back to Standard Mode.
Car Mode does not show there either.
I don't have a car with Bluetooth so can't test to see if it will appear when it recognizes a car.