Green’s Dictionary of Slang

1. (also bungo!) a toast when drinking.

1921		D.L. Sayers Unpleasantness at the Bellona Club 8: ‘Dry Martini,’ said Wimsey [...] ‘Bung-ho!’.
1925		Springfield Union 20 Nov. n.p.: They now say ‘Bungo!’ instead of ‘Here’s how!’ over cocktails.
1945		G. Fairlie Capt. Bulldog Drummond 71: ‘Bung-ho!’ [...] ‘Here,’ said Harlow solemnly, ‘is to the skin off your nose, if that is necessary.’.
1958		H.E. Bates Darling Buds of May (1985) 53: ‘Bung-ho,’ she said to the Brigadier.
1977		‘John le Carré’ Honourable Schoolboy 133: Frost drank greedily [...] ‘Bung-ho.’.

2. a farewell, goodbye.

1923		O. Onions Peace in Our Time 75: ‘Bung-ho, you chaps—’ ‘Bung-ho, Miss Massingham.’.
1934		Wodehouse Right Ho, Jeeves 99: Some of my pals [...] if turned down by a girl, would simply say, ‘Well, bung-ho!’ and toddle off quite happily to find another.
1948		J. Betjeman ‘Beside the Seaside’ in Coll. Poems (1958) 152: ‘Farewell,’ ‘So long,’ ‘Bunghosky,’ ‘Cheeribye’.