I just tested my "low flow" shower head to see how much water it used as compared to a bath. I've always had my doubts as to the veracity of the claims that many shower head makers make about water savings with showers. The one I have is a WaterPik EcoFlow® VBE-423. It is 1.5 gallons a minute. I just left the stopper in and compared the amount of water I ended up with to how much water I would use for a bath. I used the water saver device during the soaping up part. That is a button on the side of the shower head that cuts down the water flow to save water when you are not actually rinsing off or getting wet.
I have to say I was surprised. The amount of water I ended up with was about a third of what I would have used with a bath. Maybe a bit more. It depends on the bath and whether it's a "hot soak" or just a bath and since I only use the bath for hot soaks I use a bit more water than is strictly needed. Regardless the savings seemed significant and I don't think not using the water saving button during the soap up would have made a big difference.
Someone who has a "high flow" or regular shower should test this. I have always thought that a bath saved water over a regular shower. I think I remember Kohler saying the opposite. I try to conserve water as much as I can. I watch my neighbors washing their patios and porches when all they need is a broom and I must say I get a bit disgusted.