Albert Adomah's 75th-minute equaliser earned Barnet a point after they came from behind three times.
Bradford opened the scoring when Barry Conlon rounded off a four-man move, but Barnet equalised when John O'Flynn took advantage of defensive confusion.
Peter Thorne restored Bradford's lead but two minutes later Nicky Nicolau netted from the edge of the box.
Conlon's close-range volley made it 3-2 at the break but Barnet deserved their second-half equaliser.
Bradford: Evans, Moncur, Tom Clarke, Lee, O'Brien, Law, Furman (Nix 73), McLaren, Michael Boulding, Conlon, Thorne. Subs Not Used: Arnison, Matthew Clarke, McLaughlan, Osborne.
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