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He allegedly launched a verbal assault on match officials when Curtis Woodhouse was sent off during the second half of the game.
Woodhouse was shown the red card only three minutes after being sent on as a substitute for a challenge on Millwall's Matt Lawrence.
Phil Dowd, the referee, referred to the incident in his match report and Bruce now has 14 days in which to provide a response.
Bruce could face a fine and/or a touchline ban if he is found guilty.