Illegal dribble or not?
 

A1 ends the dribble. While holding the ball: (a) A1 touches B1 with the ball and begins to dribble again; or (b) the ball comes into contact with B1, unintentionally, during normal guarding activities by B1 and A1 begins to dribble again.

Ruling?

If A1 didn't lose control as a result of the touching by B, then it's an illegal dribble.

Always Listen To bob ...
 

9-5: A player shall not dribble a second time after his/her first dribble has ended,
unless it is after he/she has lost control because of:
ART. 1 A try for field goal.
ART. 2 A touch by an opponent.
ART. 3 A pass or fumble which has then touched, or been touched by,
another player.