Ashley Williams wasted Wales’ best chance to score late on, while Wayne Hennessey was the busier of the two goalkeepers making a number of key saves to keep out Bosnia.
The draw maintains Wales’s unbeaten start to qualifying in Group B and move them to the top of the group after two games.
Wales started on the front foot and went close to scoring after just seven minutes when Chris Gunter got down the right and crossed for Bale inside the six-yard box, but Toni Sunjic got back to clear the danger.
Bosnia created their first opening on 10 minutes when they caught the Wales defence sleeping from a quickly taken free-kick and Miralem Pjanic fired in a skidding shot from 25 yards out which Hennessey did well to push out.
Wales’ main threat Bale had a sight of goal on 13 minutes when he latched onto Ben Davies’ superb pass and tried to lift his volley over the goalkeeper only to see it fall the wrong side of the post.
The home side continued to call the tune in the early stages and the impressive Chris Gunter got on the end of Neil Taylor’s cross from the left, but volleyed his effort over the top.
Bosnia started to get more into the game the longer the half went on and Hennessey was fortunate that Vedad Ibisevic’s glancing header from a corner on 32 minutes flew straight at him rather than either side of him.
Wales survived a scare right on the stroke of half-time when Bosnia had strong claims for a penalty turned down after Ibisevic went down in the box under a challenge from James Chester.
Bosnia came flying out of the blocks at the start of the second half and Hennessey denied them the opener on 50 minutes with a brilliant point-blank save from Haris Medunjanin inside the six-yard box.
Wales found themselves under the cosh and Edin Dzeko forced Hennessey into two saves in quick succession before the impressive Medunjanin saw his curling effort from the edge of the box tipped wide by the overworked Wales goalkeeper.
Bosnia continued to look the most likely to break the deadlock and Pjanic was inches away from scoring on 68 minutes when is free-kick from the edge of the box sailed just wide of the far post.
Things threatened to boil over 20 minutes from time when Chester caught Muhamed Besic with a heavy challenge sparking clashes between both sets of players and resulted in bookings for Chester, Dzeko and Wales captain Ashley Williams.
Wales should have grabbed the lead on 78 minutes when Bale picked out the unmarked Ashley Williams inside the box with a superb cross, but the big defender nodded it over the crossbar with only Asmir Begovic to beat.
Hennessey came to Wales’s rescue ten minutes from time with a flying save to keep out Pjanic’s swerving free-kick from 30 yards out.
Bale fashioned a chance for himself on 82 minutes when he skipped past three Bosnia defenders and fired in a right-footed shot which forced Begovic into a decent save.
Real Madrid star Bale almost created a goal out of nothing in stoppage time when he fired in a swerving shot from 30 yards out which Begovic did well to tip round the post.
From the resulting corner substitute Hal Robson-Kanu got his close-range header all wrong as both sides had to settle for a point.