I imagine if you are speaking as in it was real life, the the 4th era would probably be c. 4th- Possibly 7th century IRL, and back then, during those times, there were public bathing situations, such as rivers and lakes, the only problem with this is that it polluted the water and was soon restricted in the c. 10th century when you had to use a "tub" and water to bathe instead of going to a river/lake.
-- Funny thing about this is, if you look at the water in Whiterun you notice that it is more dirty than the rivers you find outside the city, so that could suggest people might have bathed in that water at the steps to Dragonsreach.
--Also the skeleton in the water under the bridge to Dragonsreach suggests that maybe a person who wanted to bathe accidentally drowned in the water. (My own theory)