Dust your blinds regularly. Firstly tilt your slats up and dust from side to side. Then tilt your slats down and repeat. Use a feather duster, soft cloth or the vacuum cleaner brush attachment.
Should you wish to wash your blinds, you can use a mild detergent in warm water. Rinse afterwards with a clean cloth. Should your blinds fit in your bathtub, you may immerse them in water and wash with a soft cloth. Dry with a lint-free cloth or leave them tilted open to dry in the hanging position.