Acoustofluidic technologies enable precise manipulation of microscale objects using travelling and standing sound waves in physiological fluids, offering exciting capabilities for biomedical and chemical applications. In particular, surface acoustic wave-based devices have shown great promise for on-chip micromanipulation, but their planar transducer configuration limits the usable workspace near the microchannel surface. Here, we present a novel acoustofluidic platform based on a digitally addressable array of piezoelectric micromachined ultrasound transducers (PMUTs) that generate bulk acoustic waves and acoustic traps within three-dimensional (3D) fluidic chambers. Through a combination of finite element modelling and experimental measurements, we quantify the acoustic field distribution and study acoustic trap formation dynamics. We demonstrate deterministic 3D levitation of particles in water at rest and under continuous flow by generating standing acoustic waves across the height of the chamber. Each PMUT within the transducer array can be independently controlled. We leverage spatiotemporal modulation of the acoustic field for continuous planar transport of microparticle aggregates. PMUT arrays are microfabricated using conventional cleanroom techniques, thus can be readily integrated with compact fluidic systems. Our work lays the foundation for the development of reconfigurable and scalable acoustofluidic micromanipulation systems, with broad potential for lab-on-chip technologies.