According to James Wright's Historia Histrionica (1699), Burt began as a boy player with the King's Men, an apprentice of John Shank (died 1636).
As a young actor filling female roles, Burt gained particular notice for playing Clariana in Shirley's Love's Cruelty.
After the theatres closed in 1642 at the start of the English Civil War, Burt, like some other actors, joined the Royalist army supporting the cause of King Charles I.
Like fellow actors Charles Hart and Robert Shatterell, Burt served as an officer in the regiment of Prince Rupert in the early and mid-1640s.
In 1661 Burt became one of the thirteen actors who were original sharers in the newly organized King's Company under the management of Thomas Killigrew.