ASA Casebook 7.6-7
 

B1 swings and hits a ground ball. The bat hits the ball or the infielder fielding the ball.
RULING: B1 is declared out for interference.

We'd kill the ball as soon as the bat rolls into it, regardless of how gently. Would that also pertain to the bat barely touching the fielder, or do we want the bat to actually interfere before calling INT?

Once you judge there was interference, you call it. In the case play, it was pretty obvious since the bat hit the infielder. The severity of the contact between bat and player is irrelevant.

And as I'm sure you know, you don't even need contact. If the fielder ducks or jumps to avoid the bat and it affects her ability to field the ball, you've got interference.