FIG. 1 is a front/right side perspective view of a bathing enclosure showing our new design; FIG. 2 is a front elevational view thereof; FIG. 3 is a cross-sectional view taken along line 3-3 of FIG. 2 thereof; FIG. 4 is a cross-sectional view taken along line 4-4 of FIG. 2 thereof; and, FIG. 5 is a top plan view thereof. The broken lines are for illustrative purposes only and form no part of the claimed design.