A quantum dot is created within a suspended nanobridge containing a two-dimensional electron gas. The electron current through this dot exhibits well-pronounced Coulomb blockade oscillations. When surface acoustic waves (SAW) are driven through the nanobridge, Coulomb blockade peaks are shifted. To explain this feature, we derive the expressions for the quantum dot level populations and electron currents through these levels and show that SAW-induced Rabi oscillations lead to the observed phenomenology.