In BDSM a red shower is the act of bleeding on oneself or someone else. This is considered highly erotic and often times done ritualistically.
This is not inclusive of menstual blood. Menstrual blood is a "Ruby Shower"
In BDSM a Dominatrix may cut her submissive partner with a scalpel and allow the blood to drip where ever she chooses. This is a red shower.