Why does a rubber band ball bounce?

Many, or most objects will bounce given the right environment.

For example, a rock will bounce, although not very well.

Dead Blow Hammers are somewhat unique with moving particles inside that are designed to help prevent bouncing.

Bouncing are augmented by lasticity of the surface with a strong force to return to the original shape.

Rubber has high elasticity, and returns to its original shape with a strong force.

Thus a rubber band ball, made up almost entirely of rubber should bounce reasonably well.

I was going to suggest low weight. But, weight in movement is momentum, and the momentum would be conserved with a good bounce.

Note, a flat ball will tend to absorb the impact of the bounce, rather than reflecting it back (does not return to its original shape), and thus does not bounce well.