Bradford held on for a hard-fought point at Valley Parade after playing most of the game with 10 men.
Dean Windass was sent-off for the Bantams after 13 minutes, following a two-footed tackle on Neil Young.
But the Cherries, who have failed to record a league win since 9 September, failed to capitalise.
Stephen Purches and Danny Hollands were both denied by Bradford keeper Donovan Ricketts before Jermaine Johnson almost won it for the hosts with 20-yard shot.
606 DEBATE: Give your thoughts on the match
Bradford: Ricketts, Doyle, Wetherall, Ainge, Bower, Jermaine Johnson (Colbeck 84), Schumacher, Bridge-Wilkinson (Parker 72), Healy, Windass, Graham (Brown 72).
Subs Not Used: Howarth, Black.
Sent Off: Windass (13).
Bournemouth: Moss, Broadhurst, Young, Connolly, Purches, Cork (Cooper 84), Hollands, Gillett, Bertrand, Fletcher, Hayter (Pitman 89).
Subs Not Used: Stewart, Foley, Gowling.
Ref: D Foster (Tyne & Wear).