Bulls didn’t have everything their way, however, and Kyle Trout was able to open the scoring for the visitors before Welsh winger Grant struck in his first league start of the campaign.
Rowan Milnes’ improved the home advantage in the second half, then Elliot Minchella dived in by the corner flag to put the icing on the cake for the Bulls.
Luke Hooley touched down late in the day for Dewsbury but it was, in reality, a consolation score. The victory takes Bradford to sixth in the table level on 10 points with fifth-placed Leigh Centurions and Halifax, in seventh.
Rams, meanwhile, take a break from league action next Sunday with a trip to Thatto Heath in the Challenge Cup.
Bradford Bulls: Ryan, Grant, Evans, Webster, Foggin-Johnston, Lilley, Milnes, Kirk, Wildie, Crossley, Storton, Farrell, Minchella. Subs: Flanagan, Wood, Hallas, Bustin.
Dewsbury Rams: Hooley, Worrincy, Trout, Ryder, Morton, Knowles, Finn, Annakin, Day, Trout, Walshaw, Kibula, Igbenidion.Subs: Ward, Field, Sherriffe, Garratt.