Presuming the two lines below are on the main timeline, pass to beauMoves() this as a constructor argument:
import com.beauMoves;
var bm = new beauMoves( this );
Then in your beauMoves() class:
package com {
import flash.display.MovieClip;
import com.*;
public class beauMoves extends MovieClip
{
private var _mainTimeline:MovieClip;
public function beauMoves( mainTimeLine:MovieClip )
{
// constructor code
trace("BeauMoves");
_mainTimeline = mainTimeLine;
}
public function thisWorks()
{
trace("Cool Beans! This one worked");
_mainTimeline.bm.alpha = .3;
}
}
}