Tree radical on the left, the indexing radical. Cotton grows on a shrubby plant, and the radical groups 棉 with 树 tree, 林 forest, 枝 branch - locating cotton in the woody-plant section even though the fluff itself is what gets harvested.
Right side 帛 is white silk cloth - 白 white over 巾 cloth - and contributes the textile sense. Combined with the wood radical, the picture is 'wood-plant producing cloth fibre', which is exactly what the cotton plant is. The reading mián is independent of 帛's bó.
