Rossendale are up to eighth place in the National League Three North after another battling performance.
Fly half Steve Nutt kicked four penalties and two conversions as Dale recorded an eighth win of the season.
Nutt opened the scoring with a penalty but the Bees took the lead with a converted try. Another Nutt penalty and a try from Sam Greenwood, also converted, saw Dale take the lead but Bradford hit back to draw level at 13-13. But Dale took control with tries from Danny Collins and a penalty try with Nutt adding the extras. A fourth penalty rounded off the scoring for Dale.
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