A Q-tip dipped in rubbing alcohol and dabbed where the hallmark cotton balls show up dries mealy-bugs out and does no harm to African violets or the environment. Or home-made or store-bought insecticidal soap spray will be as effective and environmentally gentle for larger numbers of affected plants.
Either treatment may need to be re-applied every 7 to 10 days until the pests are gone from the plant in question.
Over-fertilizing or over-watering can encourage mealy-bug presence. The soil always should be just moist enough to leave dirt specks on a probe or ruler plunged a couple inches down from the soil surface.