Hausa provides a surely related form that may shed light on the term's history: the ethnonym būzu < *bugzu (by Klingenheben's Law, as shown by the pl. bugā̀jē) "serf of the Azben [Air] people" (Bargery). The term refers to ex-slaves, iklan, what in Mali would be called Bella. It presumably does not share an etymology with būzu pl. būzā̀yē "undressed skin mat, loin-cloth", with no *g, for which Skinner (1996) gathers plausible cognates elsewhere in Chadic.
Combining the two, we get what looks like a brief glimpse of morphology: the homeland of the *Bugzu is *Bagzan (perhaps their manufactures included crude plates). From a Tuareg perspective, -ăn looks like a masculine plural ending; but the specific vowel alternation would be hard to explain Tuareg-internally, though Tuareg has a-ablaut in other plural types. From a Chadic perspective, one is reminded of the -n plurals of Bade and Ngizim, e.g. Bade zawa-n pl. zawa-n-ən "stick" (Schuh ms), Ngizim gâzbə́r̃ pl. gázbàarín "tall" (Schuh ms, 1972); Ngizim even offers parallels for the vowel alternation, and a-ablaut plurals are widespread in Chadic more generally. The Bade-Ngizim subgroup includes geographically the closest Chadic varieties spoken to the Air besides Hausa, located almost due south of the Air, so it seems a promising point of comparison; could the *Bugzu have spoken a since lost West Chadic B.1 language? But of course, nothing guarantees that Bagzan should be an old plural; perhaps -ăn was a locative suffix, or something else entirely.
I wouldn't be surprised if some early 20th century work proposes this connection, but I haven't come across it in the literature so far; if you have, let me know.