Yeovil goalkeeper Sam Walker was on hand to deny the Cherries on numerous occasions in the opening half, with Wes Thomas and Steve Cook testing the on-loan Chelsea goalkeeper.
Cook turned past his marker and teed-up a shot for Thomas who forced a sprawling save from Walker after 27 minutes.
The 20-year-old goalkeeper again produced heroics just five minutes later when Cook rose above the Glovers' defence to meet Marc Pugh's cross and head towards the top corner only for Walker to turn the ball away.
The Cherries were left frustrated after the interval with Zavon Hines, Scott Malone, Arter and substitutes Donal McDermott and Wes Fogden all miscuing when through on goal.
The visitors rarely threatened, but will settle for the point and a first clean sheet in their last five games.