Danny Williams crossed over twice in the space of eight minutes to put the hosts well on their way, before Lee Gaskell made things even better soon after.
The contest was heading just one way when Jay Pitts joined the party just over a quarter of the way through, touching down to allow Danny Addy to successfully kick over for the second time.
Sheffield, who finished just one place behind their opponents at the end of the regular Championship season, had Misi Taulapapa to thank for dragging their way back into things shortly before the interval.
Normal service was soon resumed, however, as Adam Henry and Gaskell crashed over to put Bradford back into a commanding position.
An on-song Gaskell was not finished there, though, completing his hat-trick shortly after the hour mark to round off his impressive display.
It was then left to James Clare to complete the scoring on his home debut, making Menzie Yere's score redundant in the grand scheme of things.