Travel or not?

[Nevadaref]

Originally Posted by JB

After ending his dribble, A1 (a) attempting to throw a pass to A2, who had vacated the area on a cut to the basket. A-1 Ran and recovered the ball. Or (b) fumbles, takes two steps and recovers before the ball hits the ground.

In (a) and (b) has A1 travelled?

While the correct answers have already been provided by JR and Bob J, [(a) illegal dribble, (b) legal play] I thought that I would post a past NFHS Interp regarding this play. Perhaps it will give someone a better understanding of the situation.

2003-04 NFHS BASKETBALL RULES INTERPRETATIONS
SITUATION 6: A1 jumps from the floor and secures a defensive re-bound. A1 then pivots toward the sideline where a teammate, A2, is standing for an outlet pass. Just as A1 releases the pass, A2 turns and runs down the court. A1 throws a soft bounce pass to where A2 was standing. A1 then moves and secures the ball without dribbling.
RULING: Legal action. A1 had the pivot foot on the floor and began a dribble by throwing the ball to the floor (the bounce pass); the dribble ended when A1 secured the ball. Upon reaching the ball, A1 also could have continued the dribble. (4-15-3,4)