We present results on the acoustoelectric current driven through a quantum point contact (QPC) placed on a suspended nanobridge, which is subject to surface acoustic waves (SAWs). The magnitude of this current is much larger than that of a two-dimensional gas, and the system has enhanced sensitivity to perturbations. In particular, the current oscillations as a function of magnetic field exhibit additional features associated with the spin splitting. Furthermore, the negative voltage applied to the QPC gates induces the oscillations revealing the subband structure not seen in transport measurements at the elevated temperatures of our experiment. Near the pinch off conditions, the acoustoelectric current becomes negative which we attribute to the enhanced backscattering caused by the SAW-phonons’ absorption and emission.