Supernovae (SNe) are known producers of dust grains based on infrared emission from young supernova remnants. However, in such remnants, the reverse shock that forms as the ejecta interact with the surrounding interstellar medium (ISM) has not yet propagated back to the explosion center and the newly formed grains and the dense ejecta knots in which they are located have generally not yet been subject to the shock. Several studies have looked at the question of the survival of such grains after the ejecta knots encounter the reverse shock, however the dependence of the survival on the conditions in the surrounding ISM has not been fully explored. Here we present the results of new calculations of the evolution of SN-formed dust grains for the case of the explosion occurring inside a pre-existing hot bubble. We will look at survival fraction of the grains that make it into the ISM and the dependence on initial grain size and composition.