The young Blues defender was booked 44 minutes into the game at Upton Park on Monday which took his yellow card tally to five for the season.
He will be available for selection for Blues' FA cup 5th Round tie at Stoke this coming weekend but will be suspended for the game against fellow-relegation strugglers Sunderland at St Andrew's on Saturday, 25th February.
Bruce collected four yellow cards during his loan spell at Tranmere Rovers earlier this season.