I'm curious, what function(s) do you have your shutter button set to do? If the subject is moving quickly towards you and you want several bursts to get shots of their legs and arms in different positions - AI Servo mode (depending on the camera brand you use)?
I would like to try something different.
Shooting by focus and recompose, I use Single Shot focus. When shooting subjects moving toward or away from me, and still in Single Shot mode, I let go of the shutter release then press it again. If I am expecting a moving subject, I set to Servo mode and the camera tracks the subject, even during a burst of shots. The catch is that you have to keep an active focus point on your subject which can be a challenge with a subject that is moving quickly but erratically.