bather vs doer

bather and doer both are nouns.

Word	Noun	Adjective	Verb	Adverb
bather	Yes	No	No	No
doer	Yes	No	No	No

As nouns, doer is a hypernym of bather; that is, doer is a word with a broader meaning than bather:

Other hypernyms of bather include actor, worker.

bather (noun)	doer (noun)
a person who travels through the water by swimming	a person who acts and gets things done
a person who takes a bath