  We use gauge theory/string theory correspondence to study the bulk viscosity
of strongly coupled, mass deformed SU(N_c) N=4 supersymmetric Yang-Mills
plasma, also known as N=2^* gauge theory. For a wide range of masses we confirm
the bulk viscosity bound proposed in arXiv:0708.3459. For a certain choice of
masses, the theory undergoes a phase transition with divergent specific heat
c_V ~ |1-T_c/T|^(-1/2). We show that, although bulk viscosity rapidly grows as
T -> T_c, it remains finite in the vicinity of the critical point.
