Remove the basket portion of the bassinet from the base and set it aside. Lay a sheet of cardboard on the floor. If using a box, cut the side or front panel large enough to fit the bottom of the bassinet. Place the bassinet on the piece of cardboard.
Trace around the bottom of the bassinet with the marker on the cardboard sheet. It should resemble an elongated oval shape.This is your template for the mattress. Mark 1/2 inch inside the template and cut it out with a utility knife or scissors. The inside of the bassinet will be slightly smaller than the template. When finished cutting, place the cardboard piece inside the bassinet to check for a proper fit. It should be a little loose but will fit snugly when the blankets are added.
Place the folded blankets on top of the cardboard until it is approximately 2 inches thick. Additional blankets may be needed to make up the difference. A thicker fleece blanket makes a good substitute when running short on blankets. The blankets can be any size, not necessarily baby blankets. Larger ones can be cut in half and folded to make the 2-inch requirement.
Place the cardboard template with the folded blankets inside the king-size pillowcase. Slide it in the open end of the pillowcase and tuck the end under.
Fit the new mattress into the bassinet, tucking the edges under as you go. It should have a nice snug fit. Tuck in edges and smooth the cover. The pillowcase serves as a bassinet sheet and is removed for washing when dirty.