gehenna:

 

you're adding a liquid in solid form that's going to turn back into a liquid, diluting the drink you've got and decreasing the density of the bubbles.

 

Consider that it might have more to do with the contact angles of the substrate being added.  Ice is not a smooth surface, but more a very rough porous material - thus it provides an increased surface area for the bubbles to form. The surface bumps so to speak are referred to I think as Nucleation Sites.