What happened in the bath scene involving Mrs. Pearce and Eliza?

Eliza, coming from a very poor background, is not familiar with a bathtub or a bathroom when Henry Higgins commands Mrs. Pearce to give her a bath. At first, Eliza exclaims with a curse word because the bath water is too hot. She also screams when she sees herself in the mirror and reports that she hung a towel over it, presumably so as not to see herself naked.
Overall, however, Eliza takes to bathing. She tells Higgins that richer women have an easy and pleasurable time keeping clean, noting:

I tell you, it’s easy to clean up here. Hot and cold water on tap, just as much as you like, there is. Woolly towels, there is; and a towel horse so hot, it burns your fingers. Soft brushes to scrub yourself, and a wooden bowl of soap smelling like primroses. Now I know why ladies is so clean. Washing’s a treat for them. Wish they saw what it is for the like of me!

Shaw shows here how huge the economic divide is between upper-middle class women and women like Eliza. Eliza, though an adult, has never had a bath in house with indoor plumbing and has never had access to hot and cold running water. Shaw is emphasizing that the differences between rich and poor are not genetic, but environmental. It is nurture, not nature, that has made Eliza who she is.