See if this helps:
https://www.youtube.com/watch?v=H06_0ApzkzY
Notice the arm movement is quite small, not a big swing; that lets them play faster. There's still movement at the elbow (the arm is relaxed), but the main move is from the wrist.
Its also important that it's swing feel, so any 8th notes (upstrokes in between) are delayed. (That's a whole other skill to master, to differentiate between straight and swing rhythms.
)