The win leaves the Robins fourth in the engage Super League, just a point behind Huddersfield in third.
The Bulls started brightly and led twice in the first half, but the hosts took the lead before the interval and dominated the second period.
The Robins would take a lead into the half-time interval however: first Dobson’s cut-out pass created a try for Liam Colbon before Peter Fox did the honours for Kris Welham, Dobson converting the latter.
Bradford saw a try disallowed after the restart, and 15 minutes into the second period Rovers extended their advantage when Welham touched down a kick to the in-goal area.
The lead was extended with a well-worked try from Fox, and although Dobson missed the conversion a penalty goal all but ended the game as a contest.