Integrated photonic devices based on Si3N4 waveguides allow for the exploitation of nonlinear frequency conversion, exhibit low propagation loss, and have led to advances in compact atomic clocks, ultrafast ranging, and spectroscopy. Yet, the lack of Pockels effect presents a major challenge to achieve high-speed modulation of Si3N4. Here, microwave-frequency acousto-optic modulation is realized by exciting high-overtone bulk acoustic wave resonances (HBAR) in the photonic stack. Although HBAR is ubiquitously used in modern communication and superconducting circuits, this is the first time it has been incorporated on a photonic integrated chip. The tight vertical acoustic confinement releases the lateral design of freedom, and enables negligible cross-talk and preserving low optical loss. This hybrid HBAR nanophotonic platform can find immediate applications in topological photonics with synthetic dimensions, compact opto-electronic oscillators, and microwave-to-optical converters. As an application, a Si3N4-based optical isolator is demonstrated by spatiotemporal modulation, with over 17 dB isolation achieved. Here, the authors demonstrate acousto-optic modulation of silicon nitride microring resonators using high-overtone bulk acoustic wave resonances, allowing modulation in the GHz range via acoustic waves. As an application, an optical isolator is demonstrated with 17 dB non-reciprocity.