The League One side have already beaten Barclays Premier League sides Chelsea and Sunderland in the last two rounds, but neither match was shown on live television
All quarter-final matches are broadcast, and although the BBC will not show Bradford's home match against Sky Bet Championship Reading, fans will be able to see it live on BT Sport, who have announced the game will be free for non-subscribers to watch, on its website or on its Sky television platform
The game will be played on Saturday, March 7 with a 12.45pm kick-off and will be screened on BT Sport 1
BBC chiefs moved to defend themselves amid a tide of criticism after opting not to show the Bantams' fifth round clash with the Black Cats, which ended in a famous 2-0 victory for the home side, on Sunday, saying they had to choose before Gus Poyet's men disposed of Fulham in a fourth round replay.
However, head of BT Sport Simon Green explained his channel's decision to select the Bradford v Reading game, as well as Liverpool's home tie with Championship Blackburn the following day (kick-off 4pm).
He said: "The excitement of the FA Cup continues on BT Sport and we have two fantastic quarter-finals on the channel.
"This will be the second time that BT Sport have shown Bradford City in this year's FA Cup and because Bradford City Football Club have been very passionate about the UK seeing their amazing club run, BT Sport have decided to make the game against Reading available to everyone to watch, online, via BT TV and Sky."
The BBC will broadcast the Midlands derby between Aston Villa and West Brom at Villa Park at 5.30pm on Saturday, March 7, and the showdown between Premier League giants Manchester United and Arsenal at Old Trafford on Monday, March 9 (kick-off 7.45pm).
Saturday, March 7:
Bradford v Reading (12.45pm) BT Sport 1
Aston Villa v West Brom (5.30pm) BBC1
Sunday, March 8:
Liverpool v Blackburn (4pm) BT Sport 1
Monday, March 9:
Manchester United v Arsenal (7.45pm) BBC1
Source : PA