In 2004, composer John Bucchino received a fan letter from an unexpected source: the performer and polymath Harvey Fierstein. Mr. Bucchino, flattered by the attention, suggested they meet. Little did he know that his new fan already had lofty plans in mind.

Over dinner, Mr. Fierstein proposed that Mr. Bucchino help him turn a 1957 Paddy Chayefsky teleplay into a musical, drawing upon Gore Vidal’s film adaptation. That conversation has since given rise to the new Broadway production “A Catered Affair,” which opens on Thursday, about a Bronx couple on a collision course as they plan a lavish wedding for their daughter. Mr. Fierstein, who wrote and stars in “Affair,” was holding out for a composer-lyricist who could impart emotional urgency to a show that he felt would be compromised by conventional Broadway fare.

The 55-year-old Mr. Bucchino, despite his appearance — bespectacled and humble, he could pass for a bashful college professor — is far from conventional. His confessional songs use lyrical, sophisticated melodies to portray the everyday drama in urban living — yearning, heartbreak, and, occasionally, discovery. Despite a decades-long career, a cadre of champions that includes Stephen Sondheim and Harold Prince, and a list of collaborators that includes Patti LuPone, Audra McDonald, Deborah Voigt, Art Garfunkel, and Liza Minelli, Mr. Bucchino is far from a household name.

“He writes a song that is an entire world unto itself,” Mr. Fierstein said. The actor was introduced to Mr. Bucchino’s work after actress Julie Halston recommended the composer’s CD “Grateful,” and was impressed by the economy of Mr. Bucchino’s storytelling. Mr. Fierstein is among many converts who had never heard of Mr. Bucchino, but became hooked by only a few songs.

“How could I not have heard about somebody this talented?” the composer Stephen Schwartz, of “Wicked,” recalls asking himself back in 1987, after hearing a recording of Mr. Bucchino’s music. Mr. Schwartz called the number on the back of the tape, thinking he was dialing an independent record company, and found himself speaking directly to Mr. Bucchino, then waiting tables in Los Angeles to make ends meet. The two of them met for a jamming session, launching a friendship that has lasted more than 20 years.

It was, in fact, their friendship that would eventually cement Mr. Bucchino’s Broadway debut. Mr. Schwartz and his wife Carole had been trying to convince their friend that his songs were theatrical, despite his lifelong allegiance to pop. “My first reaction was ‘no!'” Mr. Bucchino said, referring to the prospect of working in musical theater, specifically in “A Catered Affair.”

But, persuaded by Mr. Schwartz, Mr. Bucchino took the job. Mr. Fierstein and Tony-winning director John Doyle imposed the conceit that the actors in “Affair” move fluidly from dialogue to music and back again. While this naturalistic approach first took Mr. Bucchino by surprise, he quickly recognized “the power of that vision,” resulting in songs that deftly depict how characters evolve and change their minds.

The Philadelphia-born Mr. Bucchino understands a thing or two about evolution. He became acquainted with classical music in college, and later assisted avant-garde experimentalist Joseph Byrd. But Mr. Bucchino was intent on becoming a singer-songwriter, and spent the 1970s and 1980s playing at clubs and piano bars in Los Angeles before landing a permanent gig as singer Holly Near’s accompanist. In 1992, after Mr. Sondheim responded to a tape the younger composer sent him by encouraging Mr. Bucchino to move to New York, he picked up and did so.

Mr. Bucchino soon became a regular on the city’s cabaret scene, and took part in salon-style parties populated by illustrious songwriting talent such as Adam Guettel, Michael John LaChiusa, Andrew Lippa, and Jason Robert Brown. “It was a magical time,” Mr. Bucchino, who finally caved in to his friends’ exhortations to write for theater, recalled. A collection of one-acts, “Urban Myths,” came next, and an excerpt — “Lavender Girl” — was subsequently directed by Harold Prince.

Since the debut of “A Catered Affair” at San Diego’s Old Globe last fall, Mr. Bucchino can no longer deny that he might be a thespian after all. “I’ve always treated my songs as if they were my diary,” the composer said. For “Affair,” he merely had to imagine “writing in someone else’s journal.”