Moisten a fresh dryer sheet with water. Wipe down the interior of the dryer. Use a clean dryer sheet once one becomes filled with dye. Continue this process until no more blue dye is coming off onto the dryer sheets.
Wash the inside of the drum with a rag and warm, soapy water. Rinse and wring out the rag as it becomes filled with dye. Continue doing this until the rag comes out clean. Rinse the drum with a rag and plain water, then dry it thoroughly.
Put a small load of old rags and towels into the dryer and run it through a complete cycle. If the laundry comes out with no blue, the dye is gone. If not, wash out the drum again with soapy water and run another test load until you are sure all of the dye is off of the drum.