Double Dribble or Out-of-Bounds?

[Rock'nRef]

Had this happen in a game this week and am hoping for a clear answer to take to my chapter meeting tonight:
Player A1 is in front court, ends dribble and is trapped by two defenders. Player A1 panics and attempts to dribble around defender. However, as player A1 begins dribble, the ball hits the defender's foot and goes out of bounds (it clearly was not an intentional attempt to throw it off of the defender) . My thought was that the defense should be awarded here for good play. The real question to me is determining what started the 2nd dribble attempt. Was it when the ball left player A1's hand or would the ball have had to hit the floor after leaving A1's hand to be considered a dribble? Thanks