Green’s Dictionary of Slang

a blow; esp. in phr. bung in the eye, a blow in the eye.

1822		Commercial Advertiser (N.Y.) 6 July 2/3–4: And there a ghastly throng of battered heads, bunged eyes, broken jaws, and demolished noses, ‘frowned in melancholy perspective,’ pleading like dumb mouths for vengeance.
1902		A.N. Lyons Hookey 23: ‘Only yesterday,’ said he, ‘I got another bung in the eye.’.