One of the key components of the susceptibility to cognitive biases is the ability to monitor for conflict that may arise between intuitively cued "heuristic" answers and logical principles. While there is evidence that people differ in their ability to detect such conflicts, it is not clear which individual factors are driving these differences. In the present large-scale study (N = 399) we explored the role of cognitive ability, thinking dispositions, numeracy, cognitive reflection, and mindware instantiation (i.e. knowledge of logical principles) as potential predictors of individual differences in conflict detection ability and overall accuracy on a battery of reasoning problems. Results showed that mindware instantiation was the single best predictor of both conflict detection efficiency and reasoning accuracy. Cognitive reflection, thinking dispositions, numeracy, and cognitive ability played a significant but smaller role. The full regression model accounted for 40% of the variance in overall reasoning accuracy, but only 7% of the variance in conflict detection efficiency. We discuss the implications of these findings for popular process models of bias susceptibility.