If bumblebees were propelled the way fixed-wing aircraft are propelled, their wings would not be aerodynamic. An airplane needs two devices to become and remain airborne. Its engines generate thrust, and its wings provide lift.
A bumblebee, however combines both thrust and lift into one integrated device. The bumblebee's wings, unlike a fixed wing aircraft, and unlike even a helicopter's blades, operate independently of each other. They oscillate, rather than rotate, and create a powerful vortex above them that generates considerably more lift than a fixed-wing aircraft, and their independent wings create more maneuverability than a helicopter's fixed blades.
An Oxford University team put bumblebees in a wind tunnel and studied the effect produced by the bumblebee's wings: http://www.sciencedaily.com/releases/2009/05/090507194511.htm. Here is an abstract of the actual study: http://link.springer.com/article/10.1007%2Fs00348-009-0631-8.
Although a bumblebee is an inefficient flyer, it's large thorax and nectar-fueled energy consumption overcome the small size of its wings.