Stellar feedback-driven outflows are important regulators of the gas-star formation cycle. However, resolving outflow physics requires high-resolution observations that can only be achieved in very nearby galaxies, making suitable targets rare. We present the first results from the new VLT/MUSE large programme MAUVE (MUSE and ALMA Unveiling the Virgo Environment), which aims to understand the gas-star formation cycle within the context of the Virgo cluster environment. Outflows are a key part of this cycle, and we focus on the peculiar galaxy NGC 4383, which hosts a $\sim\!\! 6\,$ kpc bipolar outflow fuelled by one of Virgo's most H I-rich discs. The spectacular MUSE data reveal the clumpy structure and complex kinematics of the ionized gas in this M82-like outflow at 100 pc resolution. Using the ionized gas geometry and kinematics, we constrain the opening half-angle to θ = 25-35°, while the average outflow velocity is $\sim\!\! 210\ \text{km} \, \text{s}^{-1}$. The emission line ratios reveal an ionization structure where photoionization is the dominant excitation process. The outflowing gas shows a marginally elevated gas-phase oxygen abundance compared to the disc but lower than the central starburst, highlighting the contribution of mixing between the ejected and entrained gas. Making some assumptions about the outflow geometry, we estimate an integrated mass outflow rate of $\sim\!\! 1.8~\mathrm{M}_{\odot } \, \mathrm{yr}^{-1}$ and a corresponding mass-loading factor in the range of 1.7-2.3. NGC 4383 is a useful addition to the few nearby examples of well-resolved outflows, and will provide a useful baseline for quantifying the role of outflows within the Virgo cluster.