The bat hitting the ball in and of itself is not automatically INT if it does not actually interfere with a fielder's ability to make a play.

From 7-3-6

ART. 6... If the bat breaks and is hit by the ball or hits a runner or a fielder, no interference shall be called. If a whole bat is thrown and interferes with a defensive player attempting a play, interference will be called.

You as umpire have to judge that there was in fact INT.