We describe a simple study of how bumblebees (Bombus spp.) behave when visiting florets which are arranged in a circle around a vertical inflorescence. In four species of bees, individuals showed a tendency for rotation in the same direction around each inflorescence on successive visits, i.e., each individual tended to go either clockwise or anticlockwise. Similar behavior has also been observed in mammals including humans. The implications of this tendency to repeat tasks in the same way are discussed, particularly in relation to our understanding of the phenomenon known as flower constancy. In humans, the tendency for individuals to turn in a particular direction is strongly related to handedness. In three of the four bee species there was a significant overall tendency for the bees to rotate in a preferred direction, suggesting that they too may exhibit handedness.