Rovers picked up a worthy point on their travels with a hardworking draw at the Goldsands Stadium.
After a first half in which neither side created anything meaningful, the game was a livelier affair after the break with more clear-cut openings.
Rovers were resolute in defence but on the odd occasion that the Cherries breached the back four, they found no way past goalkeeper Jason Steele.
The stopper denied Yann Kermogant with a full length save from the forward's header, before an even more impressive stop to keep out a Harry Arter attempt.
The home side went closer when they struck the bar through Kermogant, but as the game entered the latter stages it was Rovers who could have grabbed all three points as Tom Cairney and Rudy Gestede were inches away.
But after shutting out Bournemouth on home soil for the first time this season, Rovers will be delighted to make the long journey home with a share of the spoils.
After the kick-off was delayed by 30 minutes due to a road accident in the vicinity of the Stadium, it was a largely uneventful first half as both sides cancelled each other out.
The blustery conditions on the South coast certainly didn't help proceedings with only half chances on offer for both clubs.
The Cherries forced Jason Steele into an early save after seven minutes when Marc Pugh fired goalwards. Whilst Chris Taylor, one of three Rovers changes from the midweek match against Norwich, screwed a shot well wide of goal following neat link-up play with Rudy Gestede.
The home side earned plenty of corners, but it was Rovers who threatened more with theirs, Gestede twice connecting with outswingers from Craig Conway, but neither troubled Artur Boruc in the Bournemouth goal.
Matt Kilgallon, captain for the day with Grant Hanley ruled out through injury, then defended excellently to prevent striker Callum Wilson getting in on goal. Harry Arter summing up the home side's frustrations with a long-range strike that was never going to trouble Steele's goal.
The first half ended with a half chance for Rovers as an overlapping Adam Henley sent a high ball to the back post, but although Ben Marshall met the ball well with a header at the back post, it couldn't beat Boruc.
Rovers will have been the happier of the two sides at the break, but neither deserved more.
At the start of the second half Rovers felt their opponents should have been down to ten men after Arter caught Taylor with a two-footed challenge in midfield. The Irishman perhaps fortunate to be only shown a yellow card.
That gave the game much more of an edge than was on view in the first half, with more urgency showed by both sides.
A whipped free-kick from Ryan Fraser caused danger with Rovers scrambling it away, whilst at the other end a Marshall centre was just cleared behind with Evans threatening.
The resulting corner was twice blocked with the ball coming out to the Northern Ireland international but he dragged his low shot well wide.
With the home side seeing more of the ball as the half wore on, Rovers made a double change to impose themselves further. Jordan Rhodes and Lee Williamson on for Chris Taylor and Jay Spearing.
Instead it was the home side who threatened further, a Charlie Daniels cross picked out Yann Kermogant in front of goal but Steele, at full stretch, dived to his left to make the save.
Rovers were living on their nerves with Gestede having to twice head away dangerous balls in the box. The visitors then thankful when Kermogant headed against the bar after the excellent Adam Henley slipped.
Three minutes from the 90 Steele had to produce another fantastic save to keep out a low strike from Arter, the Rovers stopper diving to his right to push the shot aside.
Despite the pressure from the home side it was Rovers, backed by a superb vocal travelling support, who had two great chances to steal the points at the death.
Tom Cairney had rarely been involved after coming on as Rovers' final sub with ten minutes to go, but right on 90 the midfielder let fly from outside the box, his shot beat Boruc, but the ball flashed inches the wrong side of the post.
Then with almost the last kick of the game Rovers threatened once more, Rhodes sent a ball into the area which Gestede met, but the header bounced agonisingly wide.
It had been a hardworking display from Rovers, their performance more than merited the point taken.
AFC BOURNEMOUTH: Boruc, Francis, Cook, Elphick (c), Daniels, Arter, Fraser, Wilson (sub Rantie 84 mins), Kermogant, Surman, Pugh (sub Ritchie 56 mins).
Subs not used: Camp (GK), Pitman, Ward, MacDonald, Smith.
ROVERS: Steele, Henley, Baptiste, Kilgallon (c), Olsson, Marshall (sub Cairney 79 mins), Spearing (sub Williamson 73 mins), Evans, Conway, Taylor (sub Rhodes 73 mins), Gestede.
Subs not used: Eastwood (GK), Spurr, Dunn, Brown.
Attendance: 10,196 (including 756 Rovers supporters).