Bryant was originally an actor and appeared in the 1950s soap opera The Grove Family. Later, he became a BBC Radio announcer while writing radio scripts as a sideline. This led to him becoming a script Editor in the Radio Drama Department and eventually the head of the Drama Script Unit. In 1967 he transferred from radio to television, where Head of Serials Shaun Sutton put him to work with script Editor Gerry Davis on Doctor Who as a "Story Associate" then story Editor.

Having acted as Associate Producer on The Faceless Ones and The Evil of the Daleks, Bryant was tested out as full Producer for The Tomb of the Cybermen, replacing Innes Lloyd, and later became full-time Producer for the later Patrick Troughton stories from The Web of Fear to The Space Pirates. Bryant was also the script Editor on the last 4 episodes of The Evil of the Daleks and the whole of The Abominable Snowmen, The Ice Warriors and The Enemy of the World. One of Bryant's last contributions to Doctor Who was the casting in June 1969 of Jon Pertwee as the Third Doctor. After the casting of Jon Pertwee as the new Doctor, Bryant left Doctor Who to become the new Producer of Paul Temple, following the departure of Alan Bromly. Bryant soon brought over Derrick Sherwin to join him on Paul Temple. Bryant and Sherwin had previously worked together on Doctor Who.