The result means Mark Yates' side will face Northampton Town over two legs in the npower League Two play-off semi final.
The Robins started the fixture with the same line-up that secured three-points against Exeter last weekend. On-loan striker Paul Benson returned following an ankle injury as the only change to the 18-man squad but started on the bench.
They home side started the day knowing they were guaranteed a play-off spot. However, if Aldershot could do them a favour against Rotherham, they could potentially still secure an automatic promotion place.
The Bantams were expected to rest one or two players for their upcoming play-off campaign but the visitors made eight changes to the side that won against Burton seven days ago.
It was a slow start to the game for both sides but Cheltenham were inches from taking the lead on quarter of an hour.
Sido Jombatti won a free kick five meters the corner flag after tangling with the Bantams' left back Carl McHugh. The resulting free kick was taken by Jones, his cross was met by the head of Steve Elliot but the big centre back couldn't direct his headed effort on target.
Jombatti had started the game brightly, shortly after he had beaten two defenders to find himself in the visitors 18-yard box and lofted the ball towards the back post. His clever ball was met by the head of Kaid Mohamed but his attempt on target didn't trouble Matt Duke in the Bradford goal as it went wide-left of the visitors upright.
The home side were having the better of the opportunities in the opening period. Jombatti beat his defender but his shot from 20-yards out was fired well wide of goal and Marlon Pack was able to force an unconvincing save from Duke, the keeper diving to his right to prevent Pack scoring from his 30-yard free kick.
Zavon Hines looked dangerous for the visitors, he was able to win corners for the Bantams but they eventually came to nothing.
Jones' almost came close to taking an unlikely lead with five minutes remaining of the half. Andrew Davies was awarded a yellow card by referee Andy D'Urso following a foul on Robins striker Byron Harrison. Billy Jones took the resulting free kick, his powerful cross passed over everyone and had to be pushed out of play by Bantams keeper Matt Duke.
Mohamed took the following corner and forced a fingertip save from Duke with his curling cross. His save fell to the feet of an off-balance Steve Elliott who scuffed his shot back across the six-yard box.
Half Time: Cheltenham Town 0-0 Bradford City
The Bradford fans were in great voice at the start of the second half despite neither side were really giving their fans anything to shot about.
That all changed on the hour mark, the Bantams were silenced as Andy D'Urso sent off Andrew Davies as he picked up a second yellow card as he pushed Kaid Mohamed to the floor as he advanced into the final third.
Neither side were able to create an opportunity on target in opening 20 minutes of the second half and Mark Yates responded positively on 67 minutes by replacing Taylor for on-loan striker Paul Benson.
The Robins immediately looked much more dangerous as Penn rifled a shot over the cross bar from 25-yards out.
The visitors responded well through Nathan Doyle. Hines caused problems for the home defence on the right wing, his cross found the central midfielder, Doyle, who had time to shoot but could only fire his effort back across the face of goal and well wide of Scott Brown's upright.
Harrad replaced Harrison with 18 minutes remaining and he was instantly involved latching onto a ball at the back post, unfortunately he stumbled under pressure and was unable to convert his chance.
Marlon Pack was denied by the post late on as he rose highest to get on the end of a Billy Jones corner. His headed effort left the Robins fans gasping as his headed effort rifled back off the Bantams upright.
The home side were making the most of the closing stages, Jombatti was able to rifle a shot just wide goal from 25-yards out before Benson turned in the 18-yard box and was able to find Harrad. The striker was able to shoot and his effort looked destined for the bottom left corner but Duke saved well diving to his right.
The result means that the Robins finish the league in forth place and secure two-legs against Northampton Town in the npower League Two, play off semi-final
Full Time: Cheltenham Town 0-0 Bradford City
Cheltenham Town FC (4-2-3-1): Brown; Jombati, Brown, Hector, Jones; Pack, Taylor (Benson '67), McGlashan, Penn (c)(Deering '78), Mohamed; Harrison (Harrad '73).
Subs not used: Lowe, Carter, Duffy, Roberts.
Bradford City FC (4-4-2): Duke; Darby, Davies, Nelson, Mchugh; Hines, Doyle, Ravenhill (c), Atkinson; Gray (Thompson '78), Connell (McArdle '63).
Subs not used: McLaughlin, Meredith, Hanson, Jones, Wells.
Referee: Mr. Andy D'Urso
Attendance: 5,888 (1,495 visiting fans)
Robins Star Man: Steve Elliott