Water will cause the pinecones to close up; they'll reopen after drying. Working in a well-ventilated area, fill large bin with 1 part bleach to 4 parts water.
Add cones; place smaller bin on top (to submerge the pinecones).
Let sit for 24 hours. Remove; let dry on paper towels. Line basket edge with floral stick, a gumlike tape; press cedar sprigs into stick. Place pinecones in basket.