Base of a Bathroom Hanger

FIG. 1 is a front, right-side and top perspective view of a base of a bathroom hanger showing my new design; FIG. 2 is a front elevational view thereof; FIG. 3 is a left side elevational view thereof; FIG. 4 is a right side elevational view thereof; FIG. 5 is a top plan view thereof; FIG. 6 is a bottom plan view thereof; and, FIG. 7 is a perspective view of the base of a bathroom hanger of FIG. 1 shown in a position of use with environmental subject matter. The rear of the base of a bathroom hanger is unornamented. The broken lines and unshaded areas depict portions of the base of a bathroom hanger that form no part of the claimed design. The additional broken lines in FIG. 7 depict environmental subject matter that forms no part of the claimed design.