Green’s Dictionary of Slang

bronze n.1

[var. on brass n.1 (2)]

self-confidence, arrogance, cheek.

[UK]Egan Life and Adventures of Samuel Hayward 51: Our hero, though not exactly possessing what is termed downright bronze, [...] had an easy sort of assurance.
[UK]Egan Finish to the Adventures of Tom and Jerry (1889) 66: His rustic modesty was [...] polished up by the acquirement of a little town bronze.
[UK]Egan Bk of Sports 98: He was not wanting in that confidence in his own achievements, vulgarly called bronze.