The Robins went into the game looking to cement a place in the play-off group but managed just one serious shot.
That came two minutes from time from sub Scott Murray cutting in from the right, but his on target drive drew an impressive save from Paul Henderson.
In the second half Bradford's top scorer Dean Windass fid in two shots and substitute Ben Muirhead drove a cross-shot just wide of the far post.
The late shots just about made up for a dreary first half which had lacked a spark as the two defences cancelled each other out.
Frustrations surfaced with two sets of double bookings. The first came when Bradford's Owen Morrison ploughed into wing-back Jamie Smith who retaliated.
Then, Robins player-manager Brian Tinnion and Windass - the two oldest players on the pitch - squared up to each other for another pair of yellow cards.
With defenders on top neither side caused danger near goal and visiting keeper Henderson dealt adequately with the few high balls to go his way, while his opposite number Steve Phillips was always well protected by newcomer Craig Ireland.
Ireland, on a month's loan from Peterborough and looking for a permanent move, pulled out one important stop at the cost of a corner when Andy Cooke, on his debut for Bradford, cut in from the left.
He also had a good second half as Bradford stepped up the pace looking for the extra points and Colin Todd's team had to settle for a share of the spoils.