This is not a common "shimmy". In fact, most of the time it's not even called a shimmy but it's performed to a similar beat to the one we like for shimmies and it's a steady small repetitive motion .... all to say that it's quite similar to the shimmy!
The bounce comes simply from the heel and reflects in the rest of the body.
Key point: keep the motion small and stead. Do not change your speed