We use equilibrium molecular dynamics methods to compute the shear and bulk viscosities of the pairwise additive and rigid SPC/E, TIP4P, and TIP4P/2005 water models. For the latter model it was found in a recent study (J. Chem. Phys. 2009,.131, 246101) an excellent agreement with experiment in the prediction of the shear viscosity over a range of different thermodynamic conditions. Here, we examine, for a wide range of temperatures, whether this remarkable accuracy of the TIP4P/2005 model remains in the prediction of the bulk viscosity. Moreover, we examine whether equilibrium molecular dynamics methods provide reasonable accuracy in the calculation of the bulk viscosity, as it was previously found for the shear viscosity (J. Chem. Phys. 2010, 132, 096101). We concluded that, by performing the appropriate data analysis, accurate estimates of the bulk viscosity can be obtained, while, compared to the other simple rigid/pairwise additive water models, the predictions of the TIP4P/2005 model for the bulk viscosity are significantly closer to the experiment.