High-temperature superconductor (HTS) maglev system shows a significant potential to be applied to high-speed rail transportation based on its passive stable levitation owning to the coupling between the HTS bulks and permanent magnet guideway (PMG). And as one of the key factors to guarantee the safe and stable operation of HTS maglev, the dynamic characteristics of the HTS bulks reflecting the operation performance of HTS maglev system under high-speed running conditions should be focused on. Therefore, this paper, based on H-formulation, established a finite element model of an HTS-PMG system, and assessed its feasibility by experiments. Moreover, the random free vibration of the HTS bulk caused by guideway random irregularity at high speed is also studied by this validated model. The random vibration characteristics and temperature variation of the HTS bulk at three high speeds (600 km/h, 800 km/h, and 1000 km/h) under vertical vibration, lateral vibration, and vertical-lateral coupling vibration, respectively, are compared. The results show that at high speed, vertical vibration can only cause the fluctuation of levitation height, while lateral vibration and vertical-lateral coupled vibration will affect both lateral offset and levitation height. Compared with the mere vertical or lateral vibration mode, the levitation height attenuation and temperature rise of the coupling vibration mode is greater due to more energy loss caused by magnetic flux motion, but it can be aid in the suppression of the vibration in the vertical and lateral direction. The increase of velocity intensifies the vibration strength of the HTS bulk and increases the fluctuation of the levitation height, lateral offset, and temperature rise. However, the vibration at a certain high speed causes a limited temperature rise and thus a limited influence on the bulk performance, and the HTS bulk is still in the safe operating range at a maximum speed of 1000 km/h. These conclusions are anticipated to provide some references for the future high-speed application of the HTS maglev system.