In general, singular acoustic beams travel in a straight line and expand during propagation, which limits the scope of their applications. We present a method for generating paraxial zero-order Bessel-like acoustic beams with arbitrary trajectories in water. We then add a vortex phase to obtain a first-order Bessel-like acoustic beam. This beam exhibits a combination of features of vortex, Bessel, and Airy beams. Moreover, it maintains a dark ``hole'' in the center, preserving its angular momentum, and displays resistance to diffraction, self-healing, and self-bending during propagation. Furthermore, we experimentally realize the beam using a three-dimensionally printed phase mask and observe the acoustic field distribution using the Schlieren imaging method. Finally, we realize particle trapping and transport in a curved trajectory in water.