PIE *bhe（温かい、熱い、baskと同じ）から。 元の意味は単に熱くなることで、湯浴みや水泳は語彙が発達した結果である。
英語の語源
bath
bath: [OE] Bath is a word widely dispersed among the Germanic languages (German has bad, as does Swedish). Like the others, Old English b?th goes back to a hypothetical Germanic *batham, which perhaps derives from the base *ba- (on the suffix -th see BIRTH). If this is so, it would be an indication (backed up by other derivatives of the same base, such as bake, and cognate words such as Latin fovēre ‘heat’, source of English foment) that the original notion contained in the word was of ‘heat’ rather than ‘washing’.
This is preserved in the steam bath and the Turkish bath. The original verbal derivative was bathe, which goes back to Germanic *bathōn (another derivative of which, Old Norse batha, had a reflexive form bathask, which probably lies behind English bask); use of bath as a verb dates from the 15th century. => bask, bathe
bath (n.)
Old English b?e "immersing in water, mud, etc.," also "quantity of water, etc., for bathing," from Proto-Germanic *batham (cognates: Old Norse bae, Middle Dutch bat, German bad), from PIE root *bhe- "to warm" (see fever) + Germanic *-thuz suffix indicating "act, process, condition" (as in birth, death). Original sense was of heating, not immersing in water. The city in Somerset, England (Old English Baeun) was so called from its hot springs. Bath salts attested from 1875 (Dr. Julius Braun, "On the Curative Effects of Baths and Waters").
例文
1. Try a hot bath with some relaxing bath oil.
ゆっくり入浴オイルで熱いお風呂に入りましょう。
2.I would love a hot bath and clean clothes.
熱いシャワーを浴びて、きれいな服に着替えてくれるといいですね。
3.They would flap bath towels from their balconies as they chatted.
彼らはおしゃべりをしているとベランダでバスタオルを振り回します。
4.The three children all bath in the same bath water.