Over the last decade, several studies have shown the importance of trait diversity in natural populations. Theoretical ecological studies are beginning to incorporate trait variations in models but they continue to be largely ignored in the context of ecosystems that exhibit alternative stable states. Here, we begin with a mean-field model of bistable savanna-woodland system and then introduce trait variation in functional and demographic traits of savanna trees and saplings in the model. Our study reveals that higher trait variation reduces the extent of bistability in the system, such that the woodland state is favoured; that is, woodland occurs over a wider range of driver values compared to the grassland state. We find that the shift from one state to another can become less or more drastic, depending on the trait which exhibits variation. Interestingly, we find that even if the overall tree and grass cover remain insensitive to different initial conditions, the steady-state population trait distribution exhibits sensitivity to initial conditions. Our model findings suggest that in dryland ecosystems, and potentially in a broader class of bistable ecosystems, historical contingency has a stronger impact at the population level rather than at the ecosystem level when trait diversity is considered.