A noun appearing as G. soth “bath” in the Gnomish Lexicon of the 1910s derived from primitive ᴱ✶sou̯þ- (GL/68), where ou became ō as was usual in Gnomish of the 1910s.
Neo-Sindarin: In later Sindarin, ancient ou became ū which would produce sûth, but since this conflicts with N. sûth “draught”, I would coin a neologism ᴺS. sûn “bath” as the cognate of ᴺQ. súnë “bath”.
A noun in the Gnomish Lexicon of the 1910s glossed “a bath”, related to the verb G. fas- “wash” (GL/34).