As usual, this kind of question is answered in Rule 4, although in this case, it's hidden in an unusual section. Instead of giving "disposal" its own definition, it's included in Section 4: "Ball Location, At Disposal".
Quote:
Art. 7 A ball is at the disposal of a player when it is:
a. Handed to a thrower or free thrower.
b. Caught by a player after it is bounced to him/her.
c. Placed on the floor at the spot.
d. Available to a player after a goal.
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So you can see that it's at the disposal of a player when it is
caught, not when it is bounced.