BrE = British English
So you say, take a bath is incorrect/not used?
No. I think he said that dropping the article is incorrect.
In the US, the expression is "take a bath" for all possible uses.
On occasion, you could possibly hear "take her bath" -- especially if there has been some prior reference to her taking a bath.
The same goes for "take a shower" -- but "take a steam" is considered a regionalism (New York City, under the influence of Yiddish, I believe.) This may account for the Hollywood locution "take a meeting."
I would not particularly react to "have a bath" however, and I might say it in certain contexts:
- The dog hasn't had a bath since his encounter with a skunk.
- I haven't had my bath yet today.
I think "having a bath" suggests the agency of some other person, while "taking a bath" suggests one's own actions.
- The infant was too sickly to have a real bath, so her mother cleaned her with baby wipes.
- Cats hate to have a bath. (Cats may have a bath, but they never take a bath.)