The relative energy loss (or gain) at each bounce. This should be left at its default value of 1.0, which is the only value with meaningful physical sense. Values bigger than 1.0 will make it impossible for GI algorithms to converge to a stable solution, and values smaller than 1.0 will have a reduction in the color bleeding effect.
Bounce Factor gives more control over GI bounces on a per shader basis rather than on a global basis via the render settings. In the following example the Bounce Factor has been changed for the shader assigned to the red sphere. When the Bounce Factor of the red sphere has been set to zero, the GI rays traced from the white floor to the sphere will not see it and therefore will not receive any color bleeding.