The story
- Proto-Indo-European*bʰeh₁-
- Proto-Germanic*baþą
- Proto-West Germanic*baþ
- Old Englishbæþ
- Middle Englishbath
- Englishbath
- Proto-Indo-European*Hrew-?
- Proto-Indo-European*(H)rewH-
- Proto-Germanic*rūmą
- Proto-West Germanic*rūm
- Old Englishrūm
- Middle Englishroum
- Englishroom
- English todaybathroom
From bath + room. Compare Dutch badkamer (“bathroom”), German Badezimmer (“bathroom”), Swedish badrum (“bathroom”), Faroese baðrúm (“bathroom”).
Etymology from Wiktionary, CC BY-SA 4.0.