Context. Current spectroscopic and photometric surveys are providing a comprehensive view of the Milky Way bulge stellar population properties with unprecedented accuracy. This in turn allows us to explore the correlation between kinematics and stellar density distribution, crucial to constrain the models of Galactic bulge formation. Aims. The Giraffe Inner Bulge Survey (GIBS) revealed the presence of a velocity dispersion peak in the central few degrees of the Galaxy by consistently measuring high velocity dispersion in the three central most fields. Due to the suboptimal distribution of these fields, all being at negative latitudes and close to each other, the shape and extension of the sigma peak is poorly constrained. In this study we address this by adding new observations distributed more uniformly and in particular including fields at positive latitudes that were missing in GIBS. Methods. Observations with Multi Unit Spectroscopic Explorer (MUSE) were collected in four fields at (l, b) = (0°, +2°), (0°, −2°), (+1°, −1°), and (−1°, +2°). Individual stellar spectra were extracted for a number of stars comprised between ~500 and ~1200, depending on the seeing and the exposure time. Velocity measurements are done by cross-correlating observed stellar spectra in the CaT region with a synthetic template, and velocity errors are obtained through Monte Carlo simulations, cross-correlating synthetic spectra with a range of different metallicities and different noise characteristics. Results. We measure the central velocity dispersion peak within a projected distance from the Galactic center of ~280 pc, reaching σV_GC ~ 140 km s⁻¹ at b = −1°. This is in agreement with the results obtained previously by GIBS at negative longitude. The central sigma peak is symmetric with respect to the Galactic plane, with a longitude extension at least as narrow as predicted by GIBS. As a result of the Monte Carlo simulations we present analytical equations for the radial velocity measurement error as a function of metallicity and signal-to-noise ratio for giant and dwarf stars.