Bolton is best known for originating the role of "The Old Man" (Mr. Parker) in the Broadway show A Christmas Story: The Musical.

[3] His other theatre credits include many Broadway musicals that have won the Tony Award including original productions of Curtains with David Hyde Pierce; Spamalot with Tim Curry, David Hyde Pierce, and Sara Ramirez, directed by Mike Nichols; Contact directed by Susan Stroman; and Titanic; and revivals of Damn Yankees and How to Succeed in Business with Matthew Broderick, with Bolton eventually playing the role of Finch opposite Sarah Jessica Parker.

A sought-after cabaret performer, Bolton has also appeared in many concert performances including Downton Abbey at 54 Below (2013),[4] Titanic reunion at Lincoln Center Avery Fisher Hall (2014),[5] and Guys and Dolls (2014) and the Family Holiday Concert with the New York Pops at Carnegie Hall.

"[6] Bolton is a regular soloist with the New York Pops, and he has headlined three sold-out concerts at Carnegie Hall.

He performed in the concert series "Broadway in the Boros" at the Queens' Socrates Sculpture Park on July 21, 2017.