My sister has always striped her baby girl down while her husband gets into the shower...... then she hands baby girl to Daddy, who showers the baby and then hands her back to Momma while he finishes his own shower. It works for them and they've done it since she was a newborn. She's two now and loves her tubby bath instead, but will still sometimes be handed to her Momma in the shower now, where she stands and showers with Mom. It works for them. I remember as a teenager, babysitting, arriving at the house, when their little four-year-old stepped out of the bathroom with one towel around her body, under her arms and another towel on wrapped (just like and adult would do) on her head! When she opened the door, billows of steam wafted out at the ceiling and amazed by this sight, I said: "Is she old enough to be taking a shower all by herself?!" Her parents laughed and said she was indeed! :)
Once they were not babies any more (over 3) my own sons preferred baths over showers, so I let them, but they were on their own once I got the tub cleaned and filled part way. I was always within earshot and they always had a great time in the tub! I miss those days of hearing laughter between brothers coming from the bathroom during bath time. I did check on them a lot too and even went in to read to them from time to time as well. Once they each hit 13 it was only showers. Then I enjoyed listening to my older son sing in the shower! He was great! Had no idea I was listening at the closed door of course! LOL! Good luck.
D.