Bathing doesn't make your periods lighter or shorter. What you may be noticing is a short-term effect: a quick, cold-water rinse can briefly reduce blood flow to the skin, and your flow returns to normal right afterward.
Next Steps
Keep bathing daily during your period as usual since it helps with hygiene and comfort. Either warm or cool water works fine, so pick whatever feels comfortable to you.
Health Tips
If your periods ever become unusually heavy, irregular or painful, please see a gynaecologist for a check.