Salford missed the chance to move off the bottom of the Super League table with their third defeat in four matches since Brian Noble took over as boss.
Noble's old club were too good for the Reds with Matty Blythe scoring two of the Bulls' five tries, with others from Luke Gale, Matt Diskin and Adrian Purtell.
Salford, beaten 36-24 at Odsal on April 1, went into the clash having conceded 98 points in their previous two matches.
The Reds were hammered 46-6 at Wigan before a 52-6 cup thumping at Warrington last Sunday.
Jordan James was out for the home side after picking up a one-match ban for a tackle on Brett Hodgson in the cup exit.
Aussie Vic Mauro returned after injury for the Reds - the only change from the Warrington ko.
However, Bradford were also lacking confidence after three successive league defeats followed by as 25-16 Tetley's Challenge Cup exit at London Broncos.
They were missing Brett Kearney, Manuse Manukatoa, James Donaldson and Adam Sidlow against his old club but handed Jacob Fairbank, on a month's loan from Huddersfield, his debut off the bench.
The Bulls went close to snatching an early lead but Nick Scruton lost the ball close to the line from a Heath L'Estrange pass.
Bradford did go in front with Jarrod Sammut taking Michael Platt's pass at speed to send Gale sprinting 60 metres to score, with Sammut booting the conversion.
A Platt mistake from Sneyd's kick allowed Ryan McGoldrick to scoot over on the half hour with Sneyd converting to make it 6-6.
Then McGoldrick edged the Reds ahead with a drop-goal after Wayne Godwin almost nipped over from dummy-half.Salford's joy was short-lived with Matty Blythe bagging two quickfire tries.
The second rower was on hand to capitalise on Sneyd's mistake from a Danny Addy kick and then took Sammut's inside pass to power through weak defence.Sammut, who was in top form at full back, landed both conversions to fire the Bulls ahead 18-7 at the break.
Play was held up eight minutes before Salford sub Nero was carried off on a stretcher with his neck in a brace.
The Bulls wrapped up victory when Diskin burrowed over on the hour to make it 24-7, before Purtell crossed two minutes from time.