I was popped right in the bath after giving birth. It stung like the dickens and the water turned purple so I can't imagine sitting around for ages in that muck.
This was in the UK though, and I don't have much experience of US hospital births, as my mother disliked them so much after three that she had her last five children at home. Still, I don't think that there is a bathing ban in force.
The only thing I've ever heard about a bathing ban is in China, where they have a baby moon. Apparently an old lady (or your mother) comes in and you are literally not allowed out for a month. No showers, no washing your hair, no teeth brushing, no cold food, you have to wear a hat all the time and they stuff you full of food and pamper you. I think they still give new mothers sponge baths or towel them down, but they are definitely not allowed to take a shower or a bath for that time.