Green’s Dictionary of Slang

b flat n.

[b n.1 (1) + SE flat]

a bedbug.

Tait’s Mag. Nov. 694: The author’s greatest suffering arose from Carlist fleas, and those insects known in polite life by the delicate name of b flats [F&H].
[UK]Dickens Household Words xx 326: A stout negro of the flat back tribe – known among comic writers as b flats.
[UK]Hotten Dict. of Modern Sl. etc. (2nd edn).
[UK]Brewer Dict. of Phrase and Fable (1903) I 80/1: B flats – bugs. The pun is ‘B’ (the initial letter), and ‘flat’, from the flatness of the obnoxious insect.
[UK]‘Old Calabar’ Won in a Canter III 99: ‘l’m bitten all to pieces — eaten up — look at my face.’ ‘Well, Sir, there is no denying as them B flats has been at you’.
T. Hughes Rugby Tennessee 58: An insect suspiciously like a British B flat.
[UK]Farmer & Henley Sl. and Its Analogues.
[US]E.H. Babbitt ‘College Words and Phrases’ in DN II:i 22: b-flat, n. Bedbug.
[UK]J. Ware Passing Eng. of the Victorian Era 13/2: B Flat (Peoples’) [...] an intimate insect (now rapidly being evicted by a survival of the fittest), which has been too fatally associated with the family of Norfolk Howard.