We make use of the Hubble Space Telescope proper-motion catalogs derived by Bellini et al. (Paper I, 2014, J/ApJ/797/115) to produce the first radial velocity dispersion profiles {sigma}(R) for blue straggler stars (BSSs) in Galactic globular clusters (GCs), as well as the first dynamical estimates for the average mass of the entire BSS population. We show that BSSs typically have lower velocity dispersions than stars with mass equal to the main-sequence turnoff mass, as one would expect for a more massive population of stars. Since GCs are expected to experience some degree of energy equipartition, we use the relation {sigma}{propto}M^-{eta}^, where {eta} is related to the degree of energy equipartition, along with our velocity dispersion profiles to estimate BSS masses. We estimate {eta} as a function of cluster relaxation from recent Monte Carlo cluster simulations by Bianchini+ (2016MNRAS.458.3644B) and then derive an average mass ratio M_BSS_/M_MSTO_=1.50+/-0.14 and an average mass M_BSS_=1.22+/-0.12M_{sun}_ from 598 BSSs across 19 GCs. The final error bars include any systematic errors that are random between different clusters, but not any potential biases inherent to our methodology. Our results are in good agreement with the average mass of M_BSS_=1.22+/-0.06M_{sun}_ for the 35 BSSs in Galactic GCs in the literature with properties that have allowed individual mass determination.