Well, ducks do need water deep enough to dunk their heads in, so they can clean their nostrils out, and they do need fresh water for drinking. Swimming water is a huge plus for ducks, but is technically not NEEDED. I provide a small stock tank and kiddie pool for my ducks, and it is fine. They certainly can swim in bathtubs as well, especially when younger.
Some important things to say though, a duckling should never be allowed access to swimming water or the tub unattended. They tire easily and can drown, or catch a chill. My ducklings are 3 weeks old and they only tolerate the tub for about 10-15 minutes with me right there, before they are cold and tuckered. Then I towel dry them and put them back under their heat lamp in their brooder.
You should also make sure their drinking water is either partially covered, or not deep enough for them to accidentally drown in.
I am not sure on what age they can swim first, but I usually allow them in at around a week or so.