Just to be very clear here, I assume we are talking about a player who has already used his dribble! After all, if he still has the dribble available, he can fumble as much as he likes, then pick it up and dribble.
By the way, do any of you give a signal, either hand or audible, that the ball has been fumbled rather than dribbled? Sometimes I think this might "explain" the reason for my not calling a double dribble on a fumble play. Not that I should have to ever explain ANY call I make.