Andy Hughes' late header rescued a draw for the Royals, but their first point in four games underlined the need for a replacement for departed manager Alan Pardew.
Everything had looked rosy for the hosts early on as they marked a lightning quick start with a goal inside five minutes.
Scott Murray ghosted past Paul Heckingbottom down the Reading right and rolled a low cross for Shaun Goater to set Steve Sidwell up for a simple sidefooted finish.
The early goal seemed to be the signal for the opening of the floodgates as the home team totally dominated.
Striker Nicky Forster was unlucky not to double the lead after a dazzling run from the halfway line and a shot which Bradford keeper Mark Paston did well to beat away.
Bradford captain David Wetharall was also forced to head off his own line after Kevin Watson had headed back a punch from keeper Paston.
But Reading's dominance collapsed following a bolt out of the blue from Bradford midfielder Paul Evans a minute before half time.
Goater inexplicably turned towards his own goal under little pressure, allowing Evans a sight of goal which prompted a stunning 30-yard shot that flew past Marcus Hahnemann.
Clearly rocked by the equaliser, Reading struggled to get back into gear in the second half and, ten minutes after the restart, a sweeping counter-attack saw Bradford take the lead.
Ben Muirhead outsprinted the back-tracking Reading defence and his neat pass set Andy Gray up for a composed finish.
Heading for a fourth successive defeat, Reading restored some pride with a frantic late finish but could only scramble a point.
Hughes hauled them level with a close-range flicked header from Nicky Shorey's driven free-kick 12 minutes from time.
But Reading were unable to force a late winner, despite seeing another two efforts cleared off the line.
Goater's close-range header was nodded away by Dean Windass and, in the dying minutes, defender Adie Williams saw a header hacked off the goal-line by Paul Heckingbottom.