The West Yorkshire outfit have developed a reputation for pulling off upsets in recent seasons, most notably seeing off Premier League leaders Chelsea in the fourth round of this year's competition, but were unable to get the better of their Championship opposition.
Pavel Pogrebnyak struck the left-hand post shortly before the half-hour mark as Reading looked to break the deadlock, but Bradford responded by finding the woodwork at the other end through Gary Liddle.
Bradford, who had scored 19 goals in six FA Cup matches this season before Saturday, looked the more likely to force a result as they dominated the second half - Andrew Davies heading just over from a free-kick with 15 minutes to go - but were unable to find a winner.
Pogrebnyak resorted to using a hand in a bid to guide the ball into the net from a late free-kick, but not even that could settle this tie as the Russian's sneaky effort rattled the post and the match ended goalless.
Phil Parkinson, who captained Reading during an 11-year stint at the club as a player, included four players who featured for Bradford on their last trip to Wembley – a 5-0 defeat to Swansea City in the 2013 League Cup final – and it was one of those men, James Hanson, who got the first effort on target.
James Meredith whipped in a cross from the left flank, but striker Hanson's header was tame and gratefully collected by Adam Federici in the Reading goal.
Bradford goalkeeper Ben Williams had to be alert when Danny Williams' 25th-minute strike from a tight angle deflected towards his near post, and Pogrebnyak turned well in the box to rifle an effort against the left-hand upright three minutes later.
Reading were beginning to turn up the heat on a Valley Parade pitch that was well-worn to say the least, but Liddle hit the post with a cross-cum-shot at the other end to remind Steve Clarke's men of the threat posed by the home side.
Filipe Morais saw a close-range effort blocked by Jordan Obita at the beginning of the second half, and the chance led to a sustained period of pressure for the hosts.
Stephen Kelly slid in to make a last-ditch challenge on an advancing Jon Stead after 65 minutes, before Hanson dragged agonisingly wide from a cross by the former Blackburn Rovers and Sunderland man.
Davies' header from a Morais set-piece caused more panic for the Reading defence, before Pogrebnyak's palmed effort from an Oliver Norwood free-kick went unpunished.
Nevertheless, the Championship side - for whom captain Alex Pearce required lengthy treatment for a bloodied nose in stoppage time - clung on to take the tie back to the Madejski, where they will be favourites to make the last four.
