There are a number of ways to remove ink stains from a dryer drum, and according to How Stuff Works, it may take a combination of these methods to remove the stain completely. The easiest way is to pour rubbing alcohol on a clean rag and rub at the stain until it disappears. You can use an ordinary non-flammable cleaner for the same result.
If rubbing alcohol doesn't work, you may need a slightly more abrasive cleaning solution. Make a paste of powdered laundry detergent and warm water. Apply the solution vigorously with a cloth until the excess dye and stains disappear. Once the ink is gone, make sure the next load of laundry will be safe from any missed ink by soaking a load of old, white towels in bleach and removing any excess liquid. Wash the towels with warm water to remove any remaining stains. Then dry the towels in your dryer. If no ink is visible on the towels, the dryer is safe for continued use. If there is still some visible ink, continue the cleaning and testing process until the towels come out clean. Wipe the dryer down one more time with a damp rag to remove any excess bleach.