If a girl bounces a ball, at what point does the ball have velocity?

An object ALWAYS has velocity, although the velocity may be zero for most of the time, or even all the time.

'Velocity' means the object's speed AND the direction in which it's moving.

As long as the girl stands and holds the ball in her hand, the ball's velocity is zero.  As soon as she drops it out of her hand, it starts having velocity that's not zero.  

While it's bouncing, its velocity is . . .

== growing and downward while it's falling from her hand toward the ground,

== zero for the instant of time when it hits the ground and changes direction from down to up,

== shrinking and upward while it's rising from the ground to her hand,

== zero for the instant of time when it hits her hand and changes direction from up to down.

moving ball hits still ball. mover stops, hit ball moves. momentum transfer.