Project leader Professor Lars Chittka, from Queen Mary University of London's School of Biological and Chemical Sciences, said: "Our study puts the final nail in the coffin of the idea that small brains constrain insects to have limited behavioural flexibility and only simple learning abilities."
The bees did not simply copy exactly what they saw, but figured out their own way to get the ball to the right destination.
"This shows an impressive amount of cognitive flexibility, especially for an insect," said Dr Olli Loukola, another member of the Queen Mary team.
During the tests, the bees had to roll a ball from the edge of the platform to the centre.
Initially, "demonstrator" bees were trained by watching a plastic bee pushing the ball to the goal.
They then moved the ball in front of other bees undergoing training, and those bees quickly learned the same trick.
But in later trials, "observer" bees that were given a a choice of three balls made a beeline for the one closest to the goal, rather than the one at the platform edge.
In yet another test they had to move a differently coloured ball to earn the reward.
Loukola said: "It may be that bumblebees, along with many other animals, have the cognitive capabilities to solve such complex tasks, but will only do so if environmental pressures are applied to necessitate such behaviours."
The research is described in the latest issue of the journal Science.