Cut a 24-by-18-inch rectangle of prequilted fabric for each place mat. Round the corners of the mat, cutting off 1/2 inch at each corner. This will make it easier to wrap the bias tape around them.
Cut an 85-inch length of double-fold bias tape, and unfold the center fold.
Wrap the tape around the edges of the mat, starting in the middle of a long side. The edges of the mat will run along the center fold, and the other folds will be on the front and back of the mat. Pin the tape in place. Fold under 1/2 inch on the final end to create a finished edge. The final end should overlap the first end by 1 inch. Cut off any excess tape.
Sew the tape to the mat by stitching 1/8 inch from the inside folds. Be sure to catch the fold on the back of the mat in the seam as well. Remove the pins as you sew.