The Doctor first used the super drive when he and Jo Grant needed to reach the village of Wootton from a distance of 72.9 miles before 2 o'clock, when the Master would perform an experiment to release Kronos. The Doctor decided to activate Bessie's super drive and flung the car into outrageously high speeds. Jo insisted that it was dangerous for the Doctor to drive at the dangerous velocity he was going, but he assured her that his reactions were ten times faster than hers (though this may have been only a boast), then hit the brakes on Bessie to demonstrate how well it could absorb inertia, whereas a normal car would have sent them through the windshield.
The Doctor later used it second time on that same day when Brigadier Lethbridge-Stewart discounted Bessie's reliability and declined a ride in the vehicle. The Doctor immediately threw Bessie in super drive and easily overtook the Brigadier's Land Rover, needling him back for his mockery. (TV: The Time Monster)
The third time the Doctor used super drive was to quickly arrive at Global Chemicals after the Brigadier had waited on him for a while, the Doctor having made an excursion to Metebelis III which took longer than expected. (TV: The Green Death)