In Ps. 51:4 and 9,Wash me thoroughly from mine iniquity, and cleanse me from my sin.
Purge me with hyssop, and I shall be clean; wash me, and I shall be whiter than snow. JPS
the verb for "wash" is כּבס but it applies only to washing clothes, not to the body. In fact, I was rather surprised (I don't know why) to find that the Gesenius Lexicon has,pr. to tread or trample with the feet, to wash garments by treading on them when underwater
and in Holladay,To full, ie. clean cloth by treading, kneading or beating
I don't know how this meaning could be translated but it certainly does not mean that God daintily wipes away the stains. It does not evoke an image of gently pouring water over our bodies in a peaceful cleansing ritual.
I'll add a comment at her post that Calvin Seerveld's rendering in Voicing God's Psalms is apt:
Scrub me utterly clean of my guilty wickedness!
Make me pure from my wasteful sin!