In the process of die-cutting bag stacks to form individual bag tops, die-cut handle apertures, or other mounting apertures, die blade configurations forming the vent lines of an array of vent apertures are also used to bond the outer surfaces of the front and rear bag walls together. The die-cutting operation selectively bonds the successive front and rear bag walls together at or adjacent the cut edges of the vent lines, thereby allowing the bags in a bag stack to subsequently self-open when dispensed.