Considerable theoretical and experimental work has lately been focused on waves localized in time and space. In optics, waves of that nature are often referred to as light bullets. The most fascinating feature of light bullets is their propagation without appreciable distortion by diffraction or dispersion. Here, analytic expressions for the fields of an ultra-short, tightly-focused and arbitrary-order Bessel pulse are derived and discussed. Propagation in an under-dense plasma, responding linearly to the fields of the pulse, is assumed throughout. The derivation stems from wave equations satisfied by the vector and scalar potentials, themselves following from the appropriate Maxwell equations and linked by the Lorentz gauge. It is demonstrated that the fields represent well a pulse of axial extension, L, and waist radius at focus, w0, both of the order of the central wavelength λ0. As an example, to lowest approximation, the pulse of order l = 2 is shown to propagate undistorted for many centimeters, in vacuum as well as in the plasma. As such, the pulse behaves like a "light bullet" and is termed a "Bessel-Bessel bullet of arbitrary order". The field expressions will help to better understand light bullets and open up avenues for their utility in potential applications.