From the NBA rule book:
A dribble is movement of the ball, caused by a player in control, who throws or taps the ball into the air or to the floor.
a. The dribble ends when the dribbler:
(1) Touches the ball simultaneously with both hands
(2) Permits the ball to come to rest while he is in control of it
(3) Tries for a field goal
(4) Throws a pass
(5) Touches the ball more than once while dribbling, before it touches the floor
(6) Loses control
(7) Allows the ball to become dead
During a dribble, there is no need to keep one bounce per step.
At the completion of a dribble, steps do matter though. It can become a travel if one takes too many steps after completion of the dribble:
- If the player receives the ball in between steps, he/she has two steps to set a pivot foot. When that pivot foot leaves the ground, the player must pass or shoot before the pivot foot touches the ground again. This effectively gives the player three steps after their last bounce of the ball if they use their third step to jump for a shot or pass.
(This is explained in Section XIV-Traveling of the rulebook.)