Green’s Dictionary of Slang

bad(d)a-bing! excl.

also ba-beem!
[echoic of suddenness]

interjection meaning ‘wham!’, ‘boom!’, ‘presto!’, ‘just like that!’.

[US]E. Torres After Hours 65: ‘[S]ome of these wops are blow-tops and sometimes even if it ain’t good for them—ba-beem! You go!’.
[US]Boston Globe (MA) 2 June 85/3: Irrera also explained the many uses of the all-purpose Italian expression ‘Badda-boom, badda-bing!’.
P. Blauner Casino Moon 192: He never liked Mike. Was always jealous [...] And the two of them had a disagreement. Botta beep, botta bing, who remembers all the details? Mike wound up dead.
[US]Detroit Free Press (MI) 4 Feb. 13D/1: After one bite of the badda Boom Badda Bing — stacked pastrami on grilled rye with Swiss cheese and Pommery mustard — my dining companion exclaims [etc].
Rutland Dly Herald (VT) 27 Feb. 5/1: ‘I said I wanted Tom Cruise,but my kids wanted Danny DeVito.’ Badda-bing, badda-boom.
[Can]Edmonton Jrnl (Alberta) 17 Sept. 1/5: [pic caption] Then — badda-bing — it was 2-1 Oilers over the Flames.
Morn. Call (Allentown, PA) 3 June Scope 3/1: Badda-bing, badda-boom everyone is a gainfully employed and living happily ever after.