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Most insects (bumblebees included) don’t simply flap their wings up and down. Each stroke (and both the up and down strokes) can be angled and turned depending on what they are trying to accomplish. Additionally they flap very fast. This combination of speed and variety of wing strokes allow many insects to change direction rapidly.
How fast are their wings? Synchronous flight muscles beat at 5 to 200 hertz (Hz), in those with asynchronous flight muscles, wing beat frequency may exceed 1000 Hz.
Not exactly about bumblebees, but this was the subject of an article on the BBC just a few days ago, though I couldn’t immediately find the original source:
Apparently they make subtle changes to each wing stroke to adjust their flight.
Being small gives you the same inherent advantages that being large gives you disadvantages: strength scales as a square of “size” (e.g. height), while mass scales as the cube. You know how you physically can’t get titanically large because eventually your muscles physically can’t be strong enough to move you, your heart can’t be large enough or strong enough to pump your blood, etc.? Well, the smaller you get, the stronger your muscles get, in relative terms. I can guarantee you that the fact that bees are small is a significant portion of the reason they’re so nimble. Their inertia decreases more quickly with size than their muscular strength does, so they can be physically capable of much higher accelerations than larger organisms.