She's a dirty girl
I started bathing with my LO at about a week, with just water. I had to sit the the bathtub anyway to try and get my stitches to heal and being single and attachment parenting there wasn't anywhere else to put her. She loved it! I filled the tub up as high as it would go and she floated around, kicked, and I guided her back in forth in the water. We had baths together everyday. And I gave her baby massages afterward with oil to keep her skin from getting itchy.
Once she was three weeks old, I tried showering. At first she wasn't sure about all the off spray but she likes those too. I hold her on my chest facing out and stand back toward the drain. The water runs down her back. I still didn't use soap. I know most people don't shower with babies until they can sit unassisted but this just doesn't gel with my lifestyle. I need to shower everyday and it isn't going to happen if I try and wait for her to be really asleep.
Beyond that, she get's really dirty! It wasn't until a few weeks after her regular baths that I noticed that she had formed a huge bit of funk under the rolls of her neck. And under her arms.
So now we shower or bath, using a non-toxic soap and she get's the whole treatment the same time I do. When she wakes up in the morning she's covered in sweat (both mine and hers) and spends all day accumulating breast-milk in her various fat rolls, and pooping on herself. She needs to be bathed every other day at least or she smells bad.
That said, I tried using a baby bathtub the other day on a whim and she started screaming

if that that was her reaction to regular bathing I think I would be trying to minimize bathing. Needless to say that will be the last time I use that big blue screaming device.