base award
 

R1 on first, F3 playing in for bunt. B2 bunts ball past pitcher & F3, ball bounces toward where F4 was playing (but F4 moved to cover first on bunt attempt). F4 recovers/retrieves bunt and tries to throw out R1 going to third, but throws the ball oob's. B/R had already crossed first and was on his way to second when F4 threw the ball oob's.
Where to place B/R?

IF that's true and if R1 had reached second at the TOT, then it's two bases TOT -- so put BR at third and score R1. IF either runner had NOT reached the next base a TOT, then it's two bases TOP -- so put BR at second and R1 at third.

Note that it's TOT that matters, not the time the ball goes out of play.

Because the throw is the first play on a batted ball by an infielder then the key here is whether F1 or F3 had a play on the ball. If the umpire believes either F1 or F3 had a play on ball then it is two bases from time of throw, if they didn't then it is two bases from time of pitch.

On this play, if F1 or F3 had a play and if BR reached first before F4 threw the ball to third then Bob is correct award R1 home and BR third base. However, if neither F1 or F3 had a play on the ball, then it doesn't matter where the runners were when the throw was made, R1 goes to third and BR goes to second.

You need to rethink this.

A "play" on the batted ball means nothing when awarding bases on a wild throw.

From the MLBUM: "A play or attempted play is interpreted as a legitimate effort by a defensive player who has possession of the ball to actually retire a runner."