The root ᴹ√KU(Ʒ) “bow” appeared in The Etymologies of the 1930s (Ety/KUƷ), most likely a later version of ᴱ√KUVU “bend, bow” from the Qenya Lexicon of the 1910s (QL/49). One notable derivative in both periods was G. cû “bow, crescent” and N. cû “arch, crescent”, which regularly appeared as S. cû “bow” in later writings, for example in S. Laer Cú Beleg “Song of the Great Bow” (GL/27; Ety/KUƷ; S/209).
The probably-related root ᴹ√KUB “bow” appeared in the Quenya Verbal System of the 1940s (PE22/102); ᴹQ. nukumna “humbled (?under-bowed)” from this period may also be related (SD/246). In notes from the late 1950s or early 1960s Tolkien gave ✶kūma, Q. cúma and S. cû(f) next to Q. lúva “bow, bight (not for shooting)” < √LUB “bend”, so presumably cúma/cû was “bow (for shooting)” (PE17/122). Finally Q. cúna “bent, curved” appeared in notes associated with the version of the Q. Markirya poem from the late 1960s, along with a verb form cúna- “to bend” (MC/222-223).
These variations make it difficult to determine what Tolkien intended the root to mean, but for purposes of Neo-Eldarin I would assume a base root of √KU(Ʒ) or √KU(H) with perhaps a verbal variant √KUB based on its use in the 1940s, and with the primitive sense “bow, bend”.