Bathe

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Old English bathian, of Germanic origin; related to Dutch and German baden .

wiktionary

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From Middle English bathen, from Old English baþian(“to bathe, wash”), from Proto-West Germanic *baþōn, from Proto-Germanic *baþōną(“to bathe”), from Proto-Indo-European *bʰeh₁-(“to warm”). Cognate with Saterland Frisian boadje(“to bathe”), Dutch baden(“to bathe”), German Low German baden(“to bathe”), German baden(“to bathe”), Danish bade(“to bathe”), Swedish bada(“to bathe”), Icelandic baða(“to bathe”). More at bath. Compare also bask.

etymonline

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bathe (v.)

Old English baþian "to wash, lave, place in a bath, take a bath" (transitive and intransitive), from root of bath (q.v.), with different vowel sound due to i-mutation. Related: Bathed; bathing. Similar nouns in Old Norse baða, Old High German badon, German baden.