Pollinators often sequentially visit one flower type while bypassing other equally rewarding flower types in the process. Many explanations for this pattern of flower choice in pollinators, known as flower constancy, have been proposed; yet, a sufficient answer to the question of why pollinators are constant still remains elusive. We tested the hypothesis that flower constancy in pollinators is related to the number of traits distinguishing available flowers by measuring the floral selectivity (both constancy and preference) of bumblebees, Bombus impatiens, when artificial flower types differed in either colour only (variation in a single trait) or colour and other floral traits (variation in multiple traits). As expected, bees showed increased degrees of selectivity (constancy and preference) when available flower types differed in colour and other floral traits compared with when available flower types differed in colour only. In addition, bee foraging rates (measured in flowers visited per min) varied inversely with the number of variable floral traits added to colour but not with the number of colours. Together, these results are consistent with the idea that the mechanism underlying flower constancy in bumblebees is a limitation on their ability to effectively search for and/or remember multiple combinations of floral traits at the same time. We discuss the roles of floral-trait variation, flower constancy and pollinator cognitive limitations in the coevolution of flowering plants and their animal pollinators.