Where does the bat speed come from? The whip he creates with his mechanics.
People don't "have" bat speed innately. They create it with physics (and maybe some muscles, I dunno how it works, I'm just an internet poser).
In almost every high level swing there is a point where the hips are initiated, the front arm is essentially locked, and the bat is still behind the hitter. I call this the NJH position, or the power V.