NFHS 7-2-2 is substantially the same as Article 2 of the college rule: if a player (somebody in the game, not a sub or somebody sitting on the bench) is out of bounds and touches the ball, that player caused the ball to be out of bounds.
I can't tell from your description whether B1 touched the ball or whether he's a player in the proper sense. If so, then B caused the ball to go OOB, and it would be A's ball for a throw-in.
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Cheers,
mb
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