To accommodate basket handles, cut notches in short-side fabric pieces. Use chalk to mark an inverted Y shape 4 1/2 inches from 1 corner. The Y should be 3 1/2 inches long and 1 inch wide at the bottom. Snip along these lines, and fold back flaps; edge-stitch in place. Repeat, making a second notch 4 1/2 inches from the other corner.
Sew sides together: With right sides facing, stitch a long side to a short side. Repeat. Sew those sewn pieces together. Press seams open.
Sew sides to bottom: With right sides facing, carefully pin sides to bottom so all corners align, and stitch. Press top edge down 1/2 inch, and hem.
Sew ties: Fold strip edges in so they meet in the middle. Fold in half lengthwise, and sew closed. Fold 1 end of each over, and hand-stitch onto the basket liner. Fold the other, loose end over 1/4 inch twice, and sew closed.
Position liner in basket, and fold upper edge over. Tie bows around handles.