Phenotypic switching is one of the mechanisms by which bacteria thrive in ever changing environmental conditions around them. Earlier studies have shown that the application of steady high hydrostatic pressure leads to stochastic switching of mesophilic bacteria from a cellular phenotype having a normal cell cycle to another phenotype lacking cell division. Here, we have studied the dynamics of this phenotypic switching with fluctuating periodic pressure using a set of experiments and a theoretical model. Our results suggest that the phenotypic switching rate from high-pressure phenotype to low-pressure phenotype in the reversible regime is larger as compared to the switching rate from low-pressure phenotype to high-pressure phenotype. Furthermore, we find that even though the cell division and elongation are presumably regulated by a large number of genes the underlying physics of the dynamics of stochastic switching at high pressure is captured reasonably well by a simple two-state model.