After a first half almost devoid of clear-cut chances, Bradford broke through two minutes after the interval with a goal from leading scorer James Hanson.
Skipper Gary Jones swung a free-kick into the goalmouth and Hanson scored with a downward header from eight yards out after Luke Oliver had stabbed the ball into the air.
Alan Connell made up for a bad fifth-minute miss by scoring City's second goal three minutes later. Graham Stack failed to hold Kyel Reid's low, left-wing cross and Connell scooped the ball over the head of the goalkeeper.
Defender Andrew Davies added a third after 57 minutes, heading home from close range from another Jones free-kick, an only a timely tackle by Jordan Brown prevented Hanson from scoring a fourth.
The result leaves Barnet at the foot of the table with only one point from six matches.