David Ngog and Jermaine Beckford scored the goals in a 2-0 success against the Cherries.
For draw specialists Bolton it was only a second win of the season, but it gave Freedman heart.
Former Liverpool man Ngog rounded Lee Camp after 36 minutes to open the scoring with his first league goal of the campaign. The lively Beckford then sealed the three points in stoppage time when his deflected drive looped over Camp.
Freedman, who won the battle of the two youngest managers in the division, said: "With the group of players I have got and the backing of the club we can achieve whatever we want to achieve.
"We have had a disappointing start, we cannot forget that, and we have to make up for it now.
"But today we showed how much quality and determination we have got and that can spring us up the table.
"We have not been beaten that many times this season and are now looking at a team which is now six unbeaten. I feel we have enough in the dressing room to keep the run going.
"I think two-nil flattered Bournemouth in the end. We worked hard for each other and my two strikers got the goals they deserved."
Bolton could have been out of sight before half-time but Jay Spearing and Alex Baptiste were guilty of squandering opportunities.
The defeat for Bournemouth was the first time this season they have failed to score and means the club have only won once in seven games.
Charlie Daniels and Tokelo Rantie had the best chances for the home side but they never really looked like scoring.
Former Burnley boss Eddie Howe is still backing his summer record signing Rantie, who has not scored in eight games, to break his goal drought.
Howe said: "You always want your striker scoring goals regardless of who it is.
"Rantie is performing well and at the hub of the assists for us. He hasn't found the net for us but that will come in time.
"We believe in the player and we are doing a lot of work with him behind the scenes to make sure he eventually does find the net.
"When you do not win regularly we are disappointed but from my perspective I have never lost sight of where we are heading.
"This year was always going to be a difficult transition for us. We went from the wrong end of League One to the middle of the Championship but I think we deserved something from the match."