Fly Ball Mechanic Question

[MGKBLUE]

Situation is R1 at 1B. Batter hits a fly ball down the left field line. BU comes inside the diamond to check the tag up of the runner. Left fielder bobbles the ball three or four time before making the catch. Runner takes off on the first touch and is halfway to second before I as the PU call out on the catch.

Defensive team appeals that the runner left early, BU did not see the bobble and calls R1 out.

Offensive coach comes out and talks to the BU, who comes to me for help.

Conversation:

BU: The runner was halfway down the line when you call the batter out. Clearly she left early.

PU: Maybe, the ball was bobbled by the left field three or four time before the catch was made. Did you see whether the runner was off the base when the ball was first touched by the left fielder?

BU: No, I was waiting for your out call.

PU: Oh @@@@ I think you have to call her safe.

Result, R1 called safe as the BU never saw an out.

Question: After looking at the ASA and High School Mechanics Manual I cannot find where this type of situation is addressed.

What are your mechanics in this situation?