Explain the irony of Blanche's singing in the bathroom while Stanley reveals her sordid past to Stella?

Blanche spends scene 7 in yet another one of her long baths. She says they keep her cool, but the baths are also symbolic of a fruitless attempt to wash guilt and disgust off herself. Think of Lady Macbeth's "out out damn spot" scene. For Blanche the baths are a ritual purification - and Stanley's constant interruptions of her bathing are representative of his rejection of her attempts to purify.