It is a scientific fact that the height to which any object bounces depends on its elasticity. This physical property is defined as the ratio of stress (The force acing on a unit area of the ball during compaction) created on the object to the strain (change in size of the ball) which acts on it. It is independent of the density of the material.
For larger values of elasticity, the strain should be smaller for a given amount of stress. In the case of a steel ball and a rubber ball, though steel has higher than rubber, it has greater elasticity, as the strain produced in steel is much less than that in rubber, for constant stress. In the case of a bouncing steel ball and a rubber ball, even though steel has higher density than rubber, it has greater elasticity, as the strain produced in steel is much less than that in rubber, for constant stress. In the case of a bouncing steel ball, collision is elastic in which both momentum and kinetic energy are almost conserved.
That is, the energy loss is minimum. Hence the steel ball bounces to a greater height than the rubber ball.
