Acoustic bullets are defined to be waves which maintain their peak amplitude and/or general shape as they propagate in free space. A general theoretical approach is presented to investigate the space-time properties of a new class of acoustic bullets which are defined here as acoustic transient Bessel beams. The approach encompasses both baseband and modulated carrier signal wave fields. Closed form space-time expressions are developed using Fourier and Hilbert transform methods for several special cases of transient Bessel beams. The space-time source distributions for generating such wave fields from planar apertures are developed from the free space wave fields via the use of the Rayleigh surface integral solution for time-dependent fields. Finally, numerical results are presented to illustrate the general space-time characteristics of the acoustic transient Bessel beams.