Wales, who had Neil Taylor sent off for an ugly second-half challenge on Ireland skipper Seamus Coleman, enjoyed the better of the game before the red card but were hanging on as the Republic launched a late blitz, although Bale went close to snatching victory.
In the end, a 0-0 draw meant that the spoils were shared as Ireland maintained their record of not losing a home qualifier since September 2013 and Wales were able to console themselves by extending their run to just one defeat in 17 qualification matches.
Serbia edged ahead of the Republic at the top of Group D on goal difference as a result of their 3-1 win in Georgia, with Wales four points adrift alongside Austria at the halfway stage having won just one of their five games to date.
Ireland boss Martin O’Neill, whose squad was severely depleted by injury and suspension in the run-up to the game, was dealt a fresh blow minutes before kick-off when James McCarthy, named in the team following his apparent recovery from a hamstring problem, was withdrawn and replaced by David Meyler.
Where the Republic were all sweat and brawn, Chris Coleman’s men were fluid and fluent, with midfield trio Joe Allen, Aaron Ramsey and Joe Ledley moving the ball confidently to feed wing-backs Chris Gunter and Taylor and try to bring front two Bale and Hal Robson-Kanu into play.
But by the time referee Nicola Rizzoli brought an end to the first half, two different methods had yielded much the same – largely nothing.
Bale produced the game’s first attempt on target three minutes after the restart, although his free-kick, awarded for McClean’s foul on Allen, was fielded without incident by Darren Randolph.
However, the keeper was relieved to see a blistering left-foot strike by the same man fly a foot wide of his left post seconds later after he took aim from 25 yards.
Lone striker Shane Long scuffed a 62nd-minute volley wide as belatedly Ireland made their presence felt.
But the game changed with 21 minutes remaining when, seconds after Bale had been booked for a late challenge on John O’Shea, Taylor was dismissed for an awful challenge which resulted in Coleman being carried off on a stretcher with a leg break.
Bale went agonisingly close late on with a curling effort but it remained goalless.