This has been my jam all week long!
That was by Earl Burtnett and his Biltmore Orchestra which played at the Biltmore Hotel in the 1920s-30s."Puttin' on the Ritz" was slang from back in the day. It meant "to dress fashionably" and alluded to the swanky (that's a word that feels synonymous of the era... but acccording to Merriam-Webster, it was first used in 1842... I'm such a nerd) Ritz Hotel.