The Saddlers came into the game looking to bounce back after being thrashed 5-2 at home by Swansea on Saturday.
And their cause was dealt a blow on 36 minutes when Julian Bennett was shown a straight red card for a two-footed lunge on Cherries striker Dani Rodrigues.
But despite being a man down, Walsall keeper Andy Oakes came to the rescue on numerous occasions to earn the Saddlers a point.
Paul Merson showed his Premiership class early on with a long-range effort that sailed just over the crossbar, but it was Bournemouth who were wasteful in front of goal in the first half with on-loan Andrew Surman volleying high and wide from close range after being teed up by Rodrigues.
Striker James Hayter volleyed a Brian Stock corner just over before blowing a golden chance on 35 minutes.
Hayter seized upon a poor back pass by Chris Westwood only to see keeper Oakes save his initial shot and the rebound that followed.
After Bennett's sending-off Walsall packed the defence and thwarted Bournemouth as they searched for an elusive goal.
And even when the Cherries broke down a stubborn visitors' defence, keeper Oakes was in top form.
Surman's precise ball on 54 minutes sent Rodrigues through on goal only for the Portuguese striker to be denied by the feet of Oakes.
And in the final ten minutes Bournemouth pushed men forward but were restricted to long-range efforts.
Marcus Browning's stinging shot from distance cleared the crossbar before Shaun Cooper saw a left-foot curler fall just wide of the post.
And with three minutes to go, Oakes was again alert when he tipped over James Coutts' right-foot shot.