In this work we investigate an extension of an implicit all-Mach formulation using the Volume of Fluid (VOF) method. The numerical scheme is implemented in Basilisk, an open source program widely used and extensively validated for various problems involving multiple phases in the incompressible limit that allows for Adaptive Mesh Refinement using octree grids. The numerical method is adapted to ensure that the numerical scheme exactly recovers the classical fractional step method used for incompressible fluids. The new formulation is shown to capture well the dynamic response of bubbles in a liquid by validating it in two different scenarios: (a) The linear oscillation of a bubble in a slightly compressible liquid and (b) the Rayleigh collapse problem.