You can fill the hose with a bleach/water solution OR use household hydrogen peroxide and let it set for an hour and then rinse it out well. This is the easiest method.
If you don't have a long enough tube brush to scrub the inside, use 2 lengths of wire, tie a rag between the 2 pieces and run it through the hose and then pull it back and forth from either end of the hose to scrub the section that is black.
Whichever method you use, try and let the hose air dry after use to reduce it coming back.