It is well known that, when a stationary vapor bubble is subject to a sufficiently intense acoustic field, it will grow by rectified heat transfer even in a subcooled liquid. The object of this paper is to study how translation, and the ensuing convective effects, influence this process. It is shown that, depending on the initial temperature distribution and other factors, convection can cause a destabilization of the bubble or its faster growth. Significant effects occur in parameter ranges readily encountered in practice. The phenomena described can therefore be exploited for bubble management, e.g., by increasing the condensation rate or promoting faster bubble growth and coalescence. In a saturated or a superheated liquid, heat rectification and convection reinforce each other and the bubble growth is accelerated by a translatory motion.