Context. Our view of the structure of the Milky Way and, in particular, its bulge is obscured by the intervening stars, dust, and gas in the disc. While great progress in understanding the bulge has been achieved with past and ongoing observations, the comparison of its global chemodynamical properties with respect to those of bulges seen in external galaxies has yet to be accomplished. Aims. We used the Multi Unit Spectroscopic Explorer (MUSE) instrument installed on the Very Large Telescope (VLT) to obtain spectral and imaging coverage of NGC 4710. The wide area and excellent sampling of the MUSE integral field spectrograph allows us to investigate the dynamical properties of the X-shaped bulge of NGC 4710 and compare it with the properties of the X-shaped bulge of the Milky Way. Methods. We measured the radial velocities, velocity dispersion, and stellar populations using a penalised pixel full spectral fitting technique adopting simple stellar populations models, on a 1 × 1 area centred on the bulge of NGC 4710. We constructed the velocity maps of the bulge of NGC 4710 and investigated the presence of vertical metallicity gradients. These properties were compared to those of the Milky Way bulge and to a simulated galaxy with a boxy-peanut bulge. Results. We find the line-of-sight velocity maps and 1D rotation curves of the bulge of NGC 4710 to be remarkably similar to those of the Milky Way bulge. Some specific differences that were identified are in good agreement with the expectations from variations in the bar orientation angle. The bulge of NGC 4710 has a boxy-peanut morphology with a pronounced X-shape, showing no indication of any additional spheroidally distributed bulge population, in which we measure a vertical metallicity gradient of 0.35 dex/kpc. Conclusions. The general properties of NGC 4710 are very similar to those observed in the Milky Way bulge. However, it has been suggested that the Milky Way bulge has an additional component that is comprised of the oldest, most metal-poor stars, which is not part of the boxy-peanut bulge structure. Such a population is not observed in NGC 4710, but could be hidden in the integrated light we observed.