  We study the phase diagram of two-dimensional, interacting bosons in the
presence of a correlated disorder in continuous space, using large-scale finite
temperature quantum Monte Carlo simulations. We show that the superfluid
transition is strongly protected against disorder. It remains of the
Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the
chemical potential. Moreover, we study the transport properties in the strong
disorder regime where a zero-temperature Bose-glass phase is expected. We show
that the conductance exhibits a thermally activated behavior vanishing only at
zero temperature. Our results point towards the existence of Bose bad-metal
phase as a precursor of the Bose-glass phase.
