Speaking ASA.
An "offer" (swing), as FUBLUE said, is making an attempt at the ball.
A batter merely running through the batter's box while carrying the bat is not a swing. It doesn't matter if the bat is on her shoulder or held out over the plate. If all she is doing is running and carrying, it is not a swing.
If, however, she makes an attempt at the ball while running, that is a swing.
Moving the bat toward the ball while running or swinging the bat while running would be considered an attempt.
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Tom
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