Tiny black worms in the shower are likely drain fly larvae; tips for getting rid of them include physically cleaning the drain out completely and killing any adult flies that remain. This is because they breed in the organic material that gets caught in the drain.
Adult drain flies can live for around 20 days. They measure between 1 and 1.5 millimeters, and they have hairy bodies and legs that make them look fuzzy. Their presence indicates a clogged drain in the home. Removing the organic material that they need for laying their eggs will help to get rid of them altogether.