ONlwSG

bùth m./f. [ˈb̥u̟ː], [ˈb̥uː], gen. bùtha -[ə], ‘shop; booth’ is derived by Cameron (in MacBain 1894a, 622) from ON búð 

Cameron writes ON búth.

f. ‘lodging, residence; hut; roofless shelter; tent (NO)’, 

So also Stewart (2004, 408), misreading MacLennan (≈1925), who gives ‘bùth [boo] m. “tent; cot; shop”. Eng. booth. ON búð’, and McDonald (2009, 347).

but by MacBain himself (1911) from its cognate, Eng. booth. In preferring an Old Norse derivation, Oftedal (1956, 135) points out that SG bùth may equally well be from modern English from a phonetic point of view, but that the difference in meaning points to an older loan and cannot be reconciled with MEng. bothe. He also notes (ibid.; 1972, 117–18) that the meaning ‘shop’ is found in all modern Scandinavian languages, including Icelandic and Faroese (búð).

Craigie (1894, 157) confuses SG bùth with Ir. and SG both ‘booth, hut’. While EG both is cognate with Eng. booth and ON búð (MacBain 1911, s.v. both; cf. Marstrander 1915a, 121), SG bùth is a loan from búð.