Pitman went close, while Molesley was denied, Fletch nodded over and Hollands fizzed just wide of the mark as half -time loomed.
The second half saw the visiting keeper denying Molesley again tipping a fierce shot around the post. The following corner saw Pearce hauled down in the box but the Cherries protests were ignored.
It was Molesley who looked most likely to break the deadlock, but again the keeper was equal to his shot. The visitors could have won it late on but the home side held out for a deserved point.