Firstly, the use of "take a bath" as an idiom to mean 'take a financial loss' is not particularly common. I'm a native British English speaker, one who is deeply interested in language and literature, and had never heard it before! I looked it up and you are right, it is in the dictionary, but it is the fourteenth definition, so I wouldn't worry about people assuming that is the first thing you mean, especially when there is no context to even suggest it.
Secondly, "take a bath" is predominantly American English. In British English, we are far more likely to say "have a bath". The same applies to showers.
I have never seen a 'bucket and cup' like the one you linked to - they just aren't used in England, and I don't think they are known in the USA either, at least not by the majority of people. They may be used in some subcultures I'm not aware of. There are some different ways people may have a 'bath', for example, a bed bath is an all-over wash given to a hospital patient without submerging them in a bathtub (in the USA, this is called a sponge bath). Still, if you said "I had/took a bath" to most BrEng and AmEng speakers they would assume you meant in a tub.
Other than the above, there is nothing wrong with your suggested sentence:
Yesterday, at this time, I had a bath.
You could also say:
This time yesterday, I had a bath.