Barnsley had most of the play but created few clear cut opportunities and have now gone five games without a win.
They are now sixth - the last of the play-off places - and only goal difference separates them from resurgent Oldham in seventh.
However, had they secured all three points against Bournemouth, Andy Ritchie's men could have been second in the table on goal difference.
They started positively, with Stephen McPhail and Brian Howard dominating midfield, but they were unable to grab an early goal and the longer the game went on their frustration grew.
Just after the half-hour mark Marc Richards delivered one well timed volley that was well saved at the foot of the near post by Bournemouth's impressive keeper Gareth Stewart.
Then, during a period of strong pressure, Paul Hayes had penalty appeals waved away when he appeared to be held back in the box and, four minutes before the break, Stewart pulled off a fabulous save to keep out a fierce 15-yard drive from Richards.
Barnsley thought they had made the breakthrough on the hour mark when Howard fired left footed into the far corner but Cheshire referee Scott Matheson had spotted a push by another Barnsley player on the edge of the box. He duly disallowed the goal even though his assistant, who was better positioned, had seen nothing wrong and kept his flag down.
Barnsley boss Ritchie made a change, sending on substitute striker Daniel Nardiello and he twice fired over in the closing stages.
But it was Bournemouth who almost snatched the spoils in the last minute with their first effort on target. James Hayter got in behind the Barnsley defence but saw his low drive brilliantly saved by Irish keeper Nick Colgan.