The catcher is busting out to field a batted ball 8 feet in front of him, when the (scored) runner wipes him out. The batter is at least 50 feet from 1st base.
My earlier point is that the catcher was not "busting out" from anywhere. It remains unchallenged.
According to the OP, in the time it took the bunted ball to reach the grass in front of the home plate circle and come to rest, the catcher took all of about two or three steps to travel from just behind home plate all the way to home plate. That is not "busting out."
Even with a "huge lead," the runner from third would still have needed to run some distance, perhaps 30-50 feet, to score after the ball was bunted. In that time, the catcher moved all of about about two or three steps. That is not "busting out."
The batter-runner had time, according to the OP, to lay down the bunt, clear the batter's box, and head down the line toward first base. In that time, the catcher moved about two or three steps. That is not "busting out."
One of the problems with this situation is that the OP asserts the catcher was coming out to play the ball but gives a factual description that is inconsistent with that assertion.
Whether the catcher was attempting to field the ball is a judgment call for the umpire to make. In this situation, nothing in the OP's description provides any basis to judge that the catcher, who was parked on top of the plate while the ball is at rest at least 13 feet away (not 8 feet--see my earlier post), deserves protection as a fielder in the act of attempting to field the ball.
Safe at home. Game over.