You are assuming they had "hipbaths."

If the weather is good, it's a lot less work to go bathe in the river.

Moving any water from well or river was done a bucket at a time. There is no evidence for piping the water around. In cities they would have pipes leading to central fountains.

They did not heat the bath. They heated the water one kettle-full at a time and the probable tub was a shape like a cut-down barrel, probably usually used for washing linen.

The Irish upper classes of the heroic age saved a lot of trouble by using a brazen tub by turns: first the women then the men. They added hot water as necessary.