you need to use many short line segments to draw a bezier curve. As you drag around objects, you need to constantly redraw the line.
I read through an article about bezier curves several months ago and made a test capx to play around with. There aren't many comments in there explaining what is going on...
the two most important parts are the function "DrawBezier" (which needs a start point, end point, and two control points), and DrawConnector (which just needs a start and end point, and assumes the control points line up with the start and end points).
https://www.rieperts.com/games/forum/Bezier_Curves.capx