The home had plenty of possession but not much to show for it although Mark Molesley twice went close to providing a winner against a dogged Vale side.
Molesley saw his 52nd-minute shot clip the outside of a post with goalkeeper Joe Anyon wrong-footed.
Molesley went close again two minutes later with a fierce right-foot shot from 25 yards which was pushed past a post by Anyon at full stretch.
Danny Hollands also nearly scored for Bournemouth in first-half injury time but his left-foot shot went narrowly wide of a post.
Vale became more of an attacking force towards the end and after 66 minutes a low left-foot shot from Scott Brown flashed narrowly wide.