Create two bezier curves, then a bezier circle. Select each of the curves in turn and under the ‘Curve and Surface’ panel in the editing buttons, type in the name of the bezier circle (default is ‘CurveCircle’). Then add as many points to the curves as you want to make the animation organic. Add a hook to each point in the curves (press Ctrl + H with a curve point selected and press “Add, New Empty”). then you can animate the location of all of the hooks to your liking along with the scale of the bezier circle. When you render, move the bezier circle out of frame or to a different layer. I made a quick example.
X.blend (143 KB)