As I learned from the book about Roman baths that I read, aquaeduct water was split into three different "channels" when arriving at a city, one of them being public baths and wells (opera publica). It seems that baths had cisterns and a pipe system that reached all the warm&cold baths, the natatio and the loo. Running water was a desirable thing in later Roman times, but not always the case. Unfortunately the book doesn't tell me how often they changed the water, but I guess it is also a question of prestige: if you're the building owner and people die from your polluted water, it will have a negative effect on your reputation, won't it?