Air carrier Captain reported receiving a ground proximity warning while performing a visual approach and performed corrective actions.

Narrative

On arrival to Burbank Airport our flight was vectored off of the STAR for sequencing. We were being given heading vectors and altitude assignments on an extended left base leg to Runway 33. Approximately 6 miles west of the airport we were fully configured for landing; at a selected speed of 160 kt.; on the last assigned heading and altitude with the autopilot engaged. Approximately; 2 miles west of the approach end of Runway 8 we acquired visual contact with the airport and were cleared for the visual approach. Approximately; 3 miles west of final I initiated an open descent from 2500 MSL to 1500 MSL. Unfortunately; the aircraft was not in approach mode and started to increase thrust and the descent rate in order to accelerate to 250 kt. I then disengaged the autothrottle and reduced thrust to idle. We subsequently got the GPW (Ground Proximity Warning) and I disconnected the autopilot; arrested the descent; and turned north toward direct to the airport. I believe that the GPW was triggered by the aggressive descent rate when we selected managed speed in cruise mode.