The first two recordings in Ella Fitzgerald's Songbooks were arranged by Bregman: the Cole Porter and Richard Rodgers entries.

Bregman arranged and conducted tracks such as "Let There Be Love" (Trend) for Bobby Short, "Rock-A-Bye Your Baby With A Dixie Melody" (Decca) for Jerry Lewis, and "The Wayward Wind" (Era) for Gogi Grant.

In addition, he produced a selection of his own instrumental albums, such as The Gershwin Anniversary Album, Funny Face & Other Gershwin Tunes, Swinging Kicks, Swingin' Standards, Dig Buddy in Hi-Fi, Symphony of the Golden West, Anita O'Day – Rules of the Road, and That Swing.

He was involved in creating the scores or orchestrations for several motion pictures in this period: Five Guns West (1955), Crime in the Streets and The Wild Party (both 1956), The Pajama Game (1957), including scoring all of the Bob Fosse dance numbers, The Delicate Delinquent, Born Reckless (1958), Secret of the Purple Reef (1960), and The Cat Burglar (1961).

Bregman wrote Jump Jim Crow – a musical for the Royal Shakespeare Company – and moved into London-based independent TV and film production.

He produced and directed The New-Fangled Wandering Minstrel Show, a TV special starring Olivia Newton-John and Georgie Fame.

It features an 18-piece big band of West Coast sidemen Hubert Laws, Ricky Woodard, Charles Owens, George Bohannon, Bobby Rodriguez, Patrice Rushen, Roberto Miranda, and others.