Using the zig-zag function on the sewing machine, sew around the edges of the chenille rectangle.
Measure 116 inches of bias tape and pin it around the chenille rectangle edges, making sure that the bias tape lies smoothly. Fold the corners of the bias tape around the chenille rectangle corners so that the bias tape is not bunched or bumpy.
Using the largest zig-zag stitch on the sewing machine, sew around the top edge of the bias tape along each side of the chenille bath mat. Remove pins as the sewing progresses.
To add a non-slip backing, cut 4 squares measuring 4 inches x 4 inches from a non-slip rubber drawer liner. Colors available differ by manufacturer. If the color of the chenille bath mat is not available, choose a neutral tone.
Glue the 4 squares with a glue gun to whichever side the sewer deems the "under side" of the chenille bath mat. Glue a square in each of the mat's corners.