We present the properties of magnetic fields (B-fields) in two clumps (clump 1 and clump 2), located at the waist of the bipolar H II region Sh2-201, based on JCMT SCUBA-2/POL-2 observations of 850 $μ$m polarized dust emission. We find that B-fields in the direction of the clumps are bent and compressed, showing bow-like morphologies, which we attribute to the feedback effect of the H II region on the surface of the clumps. Using the modified Davis-Chandrasekhar-Fermi method we estimate B-fields strengths of 266 $μ$G and 65 $μ$G for clump 1 and clump 2, respectively. From virial analyses and critical mass ratio estimates, we argue that clump 1 is gravitationally bound and could be undergoing collapse, whereas clump 2 is unbound and stable. We hypothesize that the interplay between thermal pressure imparted by the H II region, B-field morphologies, and the various internal pressures of the clumps (such as magnetic, turbulent, and gas thermal pressure), has the following consequences: (a) formation of clumps at the waist of the H II region; (b) progressive compression and enhancement of the B-fields in the clumps; (c) stronger B-fields will shield the clumps from erosion by the H II region and cause pressure equilibrium between the clumps and the H II region, thereby allowing expanding I-fronts to blow away from the filament ridge, forming bipolar H II regions; and (d) stronger B-fields and turbulence will be able to stabilize the clumps. A study of a larger sample of bipolar H II regions would help to determine whether our hypotheses are widely applicable.