Not 'Bowmaneer', but perhaps in some degree related to it. See threads:

Lyr ADD: The Tailor and the Louse: text and tune noted by the Hammond brothers from George Udall, Halstock, Dorset, July 1906. Also in DT at The Tailor and the Louse.

Lyr Req: The Tailor & The Mouse: text and tune from Baring-Gould and Sharp, English Folk-Songs for Schools. Derivative text and tune, from Burl Ives Song Book, in DT: The Tailor and the Mouse.

Those discussions also contain links to 'Bowmaneer' threads; all can be found via the search engine. There is some brief mention of the C18 broadside song 'A Bloody Battle between a Taylor and a Louse' and the C17 'A Dreadful Battle between a Taylor and a Louse' (mid C17, reissued later as 'The War-like Taylor'), in the notes to Classic English Folk Songs, the recent revision of The Penguin Book of English Folk Songs, for which supplementary material can be seen at Classic English Folk Songs: Supplementary material.

How far the later songs can be said to be 'related' to the earlier, as opposed to being separate compositions on a familiar theme, I wouldn't like to guess. There may, I suppose, have been some specific target intended by the broadside writers; but I don't recall authorities like Ebsworth making any suggestion along those lines. As like as not, the songs are all just swipes at a popular butt for ridicule, the tailor.