The rise of antibiotic resistance in many bacterial pathogens has been driven by the spread of a few successful strains, suggesting that some bacteria are genetically pre-disposed to evolving resistance. Here, we test this hypothesis by challenging a diverse set of 222 isolates of Staphylococcus aureus with the antibiotic ciprofloxacin in a large-scale evolution experiment. We find that a single efflux pump, norA, causes widespread variation in evolvability across isolates. Elevated norA expression potentiates evolution by increasing the fitness benefit provided by DNA topoisomerase mutations under ciprofloxacin treatment. Amplification of norA provides a further mechanism of rapid evolution in isolates from the CC398 lineage. Crucially, chemical inhibition of NorA effectively prevents the evolution of resistance in all isolates. Our study shows that pre-existing genetic diversity plays a key role in shaping resistance evolution, and it may be possible to predict which strains are likely to evolve resistance and to optimize inhibitor use to prevent this outcome.