Pitman struck four minutes before half time when he was allowed time and space on the edge of the area to curl a left footed shot past Bradford goalkeeper Matt Glennon.
The Bournemouth striker's goal was the only real chance of an even first half with both sides cancelling each other out.
Only a tame right-footed shot by Bradford's Ryan Kendall called Bournemouth's Shwan Jalal into action while his opposite number Glennon was more than equal to Pitman's 40 yard free-kick.
In a rare Bradford attack Gareth Evans almost levelled on the hour. Gavin Grant's through ball played in the striker only for his shot to come back off the crossbar.
Pitman had a chance to seal the win 20 minutes from time but his point-blank shot was well kept out by Glennon. Zesh Rehman then cleared Liam Feeney's shot off the line but one goal was enough for the home side.