According to the OED, the intransitive verb "to bathe" means "to take a bath; or to plunge or immerse oneself in water or other liquid, so as to enjoy its influence". "To bath" has also been used in the same way. The examples given include:
- 1765 W. Cowper: It is a noble Stream to bath in.
- 1863 A. P. Stanley: The princess came down..to bathe in the sacred
Note that these verbs do not necessarily imply use of a bathtub or other vessel, unless in transitive form "to bath [eg a baby]", and they don't necessarily imply washing either.
But confusingly the noun forms are used differently:
"A bath", as a noun, normally refers specifically to what in US English would be called a bathtub, namely "a vessel or receptacle intended to contain water for the purpose of bathing".
"A bathe", also as a noun, refers to the "act of bathing" and is used when the bathing is not being done in a bathtub or similar. This usage is said to be "of modern origin" - but obviously not that modern as the examples given are:
- 1827 R. Southey: A two hours' walk, and a bathe in the Greta.
- 1861 Saturday Review: A mountain stream in which the happy party
took every day their morning bathe.
The expression "to take a bath" (very similar to "had her bath" as used here) means, according to the OED, "to bathe, especially in a place or vessel prepared for the purpose" [such as a bathtub]. It its now chiefly used to mean "to wash oneself in a bath" [bathtub]:
- 1960 L. Wright: A statistician tells us that of our neighbours on
a London bus today, one in five never takes a bath.
- 2002 C. Slaughter: Take a bath, brush your hair, put on some shoes.
By analogy, "had her bathe" would mean bathed, but not in a bathtub or similar.
Quite why an editor should have changed "had her bathe" to "had her bath" is unclear, especially as it's likely to suggest to modern readers, as it apparently did to you, that some washing is involved. My guess is that someone simply 'corrected' the rather uncommon phrase "had her bathe" to the much more common "had her bath" without thinking too deeply about the potential change of meaning. A better amendment would have been "Polly went down and bathed".
In the context of the book, the change from "bathe" to "bath" wasn't I think intended to change the meaning, which evidently refers to going for a swim. There is no necessary implication of washing, dressing or attending to appearance in either case.