We present the properties of magnetic fields (B fields) in two clumps (clump 1 and clump 2), located at the waist of the bipolar HII region Sh2-201, based on James Clerk Maxwell Telescope SCUBA-2/POL-2 observations of 850{mu}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 HII region on the surface of the clumps. Using the modified Davis-Chandrasekhar-Fermi method, we estimate B-field strengths of 266 and 65{mu}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 of the thermal pressure imparted by the HII region, the B-field morphologies, and the various internal pressures of the clumps (such as magnetic, turbulent, and gas thermal pressures) has the following consequences: (a) formation of clumps at the waist of the HII region; (b) progressive compression and enhancement of the B fields in the clumps; (c) stronger B fields that will shield the clumps from erosion by the HII region and cause pressure equilibrium between the clumps and the HII region, thereby allowing expanding ionization fronts to blow away from the filament ridge, forming bipolar HII regions; and (d) stronger B fields and turbulence that will be able to stabilize the clumps. A study of a larger sample of bipolar HII regions would help to determine whether our hypotheses are widely applicable.