First-half strikes from Lee Chung-yong and Lukas Jutkiewicz had seen the home side look in complete control until a long-range Lewis Grabban goal saw the Cherries back in the game at the break.
Simon Francis then headed in a scrappy second-half equaliser to save a deserved point for the visitors.
A point sees the Trotters languishing in 19th, with the fans making their voices heard with a chorus of boos at full-time.
It was the north-west outfit's ninth game without a win, with their previous victory coming in an FA Cup tie at home to Blackpool.
Their form at home, though, is particularly worrying, as they have only taken all three points twice so far this season.
Freedman opted to give Liam Trotter his full Bolton debut after he penned permanent terms on transfer deadline day, having previously been on loan.
Meanwhile, Eddie Howe chose to keep his deadline day signing, Yann Kermorgant on the bench for a second game running.
Both teams had bright starts to the game in attack, with both Harry Arter and then Chris Eagles narrowly firing inches wide early on.
Mark Davies then provided a defence-splitting pass in a crowded box, finding Lee who blasted the ball past Lee Camp and into the roof of the net.
The second came as a hopeful punt up field by Alex Baptiste was controlled in the air by Jutkiewicz, with the striker on loan from Middlesbrough then catching Camp cold with a delightful half-volley from range. But that two goal advantage did not last long.
Despite Arter being down injured after the restart, referee Andrew Madley allowed the game to go on.
Grabban then blasted the ball into the back of the net from 30 yards to cut the deficit back to one going into half-time.
The cherries then came out in the second half the brighter and, after a near miss from Steve Cook's header from close-range on the back of Ian Harte's corner, they drew level.
Another corner from set-piece specialist Harte was latched onto this time by Francis, whose header deflected in past Adam Bogdan.
With the crowd now on their backs, Wanderers continued to look second best, as the visitors were more probing on the counter.
But, despite the Trotters coming on strong in the latter stages, it was not enough as their winless streak continued.