The quickfire Cherries steamed into a 12th minute lead through defender Karl Broadhurst before an Alan Connell goal six minutes later effectively killed the game off.
Defender Broadhurst scored his first league goal of the season when he volleyed home from ten yards after a knock down by defender Eddie Howe.
Striker Connell struck his fourth of the campaign with a piece of individual skill when he twisted past two Bradford defenders on the edge of the area before cracking a left-foot shot past keeper Paul Henderson.
Bradford had an immediate chance to pull a goal back on 21 minutes when Danny Forrest teed up Lewis Emanuel, only for his 25-yard shot to come crashing back off the bar.
Bradford keeper Henderson was called into action on 28 minutes when Warren Cummings cut in from the left to curl a shot goalwards which the youngster did well to push round the post.
But despite being on their back foot for most of the first 30 minutes it was Bradford who wasted three golden opportunities before half-time.
First Ben Muirhead dragged a shot wide from ten yards before Emanuel was denied from 25 yards by a superb reflex save by Neil Moss.
And the Bournemouth goalkeeper was again forced to save well when Steven Schumacher unleashed a 25-yard thunderbolt.
Bournemouth were dealt a blow seconds before the interval when influential defender Howe was stretchered off.
And minutes into the second half midfielder Brian Stock suffered the same fate as he was substituted for Marcus Browning.
Despite Bradford's growing possession in the second half they failed to muster a single shot on goal.
Bournemouth's only notable effort of the second half came on 72 minutes when right-back Neil Young's shot went out for a throw-in.