Why is it impossible to make a passive sentence from 'I am having a bath' while ' A good care is taken of the girl' is possible?

'A bath is being had by me' is a possible sentence. However, as you must know, it is a very awkward sentence that would never be spoken by a native speaker.

The reason that it is possible to say this sentence is that 'have' is a transitive verb. A transitive verb takes an object, in this case 'a bath.' So, you can make a passive sentence as I did above.

Yet, 'have a bath' in British English, and 'take a bath' in American English, are so idiomatic that almost no one would even consider breaking up the phrases.

You have asked a very logical question. You know how the passive is formed, but you have noticed that this particular phrase -- have a bath -- is not put into the passive. In this case, I think we can safely say that it is a matter of idiomatic usage.

Thanks a lot.