Is a batter out if a bunted ball hits the bat in fair territory for a second time?

That is a judgment decision to be made by the umpire. MLB Rule 6.5(H) states a batter is out when:
"After hitting or bunting a fair ball, his bat hits the ball a second time in fair territory. The ball is dead and no runners may advance. If the batter-runner drops his bat and the ball rolls against the bat in fair territory and, in the umpire's judgment, there was no intention to interfere with the course of the ball, the ball is alive and in play;
Rule 6.05(h) Comment: If a bat breaks and part of it is in fair territory and is hit by a batted ball or part of it hits a runner or fielder, play shall continue and no interference be called. If batted ball hits part of broken bat in foul territory, it is a foul ball.
If a whole bat is thrown into fair territory and interferes with a defensive player attempting to make a play, interference shall be called, whether intentional or not.
In cases where the batting helmet is accidentally hit with a batted or thrown ball, the ball remains in play the same as if it has not hit the helmet.
If a batted ball strikes a batting helmet or any other object foreign to the natural ground while on foul territory, it is a foul ball and the ball is dead.
If, in the umpire's judgment, there is intent on the part of a baserunner to interfere with a batted or thrown ball by dropping the helmet or throwing it at the ball, then the runner would be out, the ball dead and runners would return to last base legally touched."
The umpire must judge whether the batter intention dropped the bat in an area where it could be touched by the bunted ball. If the umpire ruled the batter did drop the bat in an area where the bunted ball would touch it, the batter is called out, otherwise, the ball is live and in play.