Dielectric measurements were carried out on suspensions of montmorillonite clay exchanged with three different counterions: sodium, ammonium, and tetramethylammonium (TMA). Only two dielectric absorption peaks could be identified for the clay sample with the TMA counterion, whereas three peaks were found for the two inorganic counterions. The dielectric process observed at around 10 GHz is due to the orientation of bulk water molecules, judging from the relaxation time and relaxation strength. The relaxation strength of the process occurring at around 10 MHz was compared with the coefficient of adiabatic compressibility obtained from ultrasound velocity measurements. The increase in the relaxation strength with decreasing compressibility indicates that the process at around 10 MHz is caused by the orientation of bound water molecules on the clay samples. The relaxation strength of the process occurring at around 10 MHz for the TMA sample was remarkably small. Furthermore, the network structure of the bound water molecules can be characterized by a property peculiar to the TMA sample, taking into account the value of its Cole-Cole parameter. Results for the relaxation strength of the process occurring at around 100 kHz were compared with those for electrophoretic mobility. This comparison revealed that discrimination between bound ions and ions in the diffuse double layer is important, and both the relaxation and electrophoretic results could be satisfactorily explained by surface polarization of the clay.