[s3e9] - The Vengeance Formulation

: To win Bernadette back after she stops returning his calls, Howard performs a grand, albeit awkward, musical apology in the middle of her workplace.

: While Bernadette is touched by the gesture, she initially rejects his subsequent marriage proposal because they had only been on three dates. However, they agree to continue dating. [S3E9] The Vengeance Formulation

In this same episode, Howard also has a notable fantasy "piece" or sequence involving (playing herself as her Battlestar Galactica character, Starbuck) while he is in a bathtub, where she helps him realize his true feelings for Bernadette. Katee Sackhoff - The Big Bang Theory Wiki | Fandom : To win Bernadette back after she stops

The "piece" you are referring to from episode " The Vengeance Formulation " (Season 3, Episode 9) is likely the song Howard Wolowitz performs for Bernadette at the Cheesecake Factory. In this same episode, Howard also has a

: Howard sings a parody version of the 1960 hit " Bernadette " by The Four Tops .