  We determine the dynamical critical exponent, $z$, appearing at the Bose
glass to superfluid transition in two dimensions by performing large scale
numerical studies of two microscopically different quantum models within the
universality class; The hard-core boson model and the quantum rotor (soft core)
model, both subject to strong on-site disorder. By performing many simulations
at different system size, $L$, and inverse temperature, $\beta$, close to the
quantum critical point, the position of the critical point and the critical
exponents, $z$, $\nu$ and $\eta$ can be determined independently of any prior
assumptions of the numerical value of $z$. This is done by a careful scaling
analysis close to the critical point with a particular focus on the temperature
dependence of the scaling functions. For the hard-core boson model we find
$z=1.88(8), \nu=0.99(3)$ and $\eta=-0.16(8)$ with a critical field of
$h_c=4.79(3)$, while for the quantum rotor model we find $z=1.99(5),
\nu=1.00(2)$ and $\eta=-0.3(1)$ with a critical hopping parameter of
$t_c=0.0760(5)$. In both cases do we find a correlation length exponent
consistent with $\nu=1$, saturating the bound $\nu\ge 2/d$ as well as a value
of $z$ significantly larger than previous studies, and for the quantum rotor
model consistent with $z=d$.
