We present a high-resolution numerical study of the phase-space diversity in an isolated Milky Way-type galaxy. Using a single N-body simulation (N ≈ 0.14 × 109) we explore the formation, evolution, and spatial variation of the phase-space spirals similar to those recently discovered by Antoja et al. in the Milky Way disk with Gaia Data Release 2 (DR2). For the first time in the literature we use a self-consistent N-body simulation of an isolated Milky Way-type galaxy to show that the phase-space spirals develop naturally from vertical oscillations driven by the buckling of the stellar bar. Thus, we claim that the physical mechanism standing behind the observed incomplete phase-space mixing process can be internal and not necessarily due to the perturbation induced by a massive satellite. In our model, the bending oscillations propagate outward and produce axisymmetric variations of the mean vertical coordinate and vertical velocity component of about 100 - 200 pc and 1 - 2 km s-1, respectively. As a consequence, the phase-space wrapping results in the formation of patterns with various morphologies across the disk, depending on the bar orientation, distance to the galactic center, and time elapsed since the bar buckling. Once bending waves appear, they are supported for a long time via disk self-gravity. Such vertical oscillations trigger the formation of various time-dependent phase-space spirals in the entire disk. The underlying physical mechanism implies the link between in-plane and vertical motion that leads directly to phase-space structures whose amplitude and shape are in remarkable agreement with those of the phase-space spirals observed in the Milky Way disk. In our isolated galaxy simulation, phase-space spirals are still distinguishable at the solar neighborhood 3 Gyr after the buckling phase. The long-lived character of the phase-space spirals generated by the bar buckling instability cast doubts on the timing argument used so far to get back to the time of the onset of the perturbation: phase-space spirals may have been caused by perturbations originated several gigayearrs ago, and not as recent as suggested so far.