If it is NCAA, it's going to be interference.....
ASA rules do not prohibit the batter/runner from carrying their bat with them. This play is governed by the rule regarding interference by a retired offensive player. I don't have the exact reference available right now.
If the umpire judges that the retired batter-runner did something to interfere with the throw to home and the defense had a chance to get the out at home, then there is interference by a retired runner, dead ball, runner closest to home is out.
The fact that the thrown ball hit the bat makes no difference in judging whether the retired batter-runner interfered with the play.