Bezier curves are drawn using two endpoints and two anchors. Drawing a Bezier curve with this information is very easy. Getting these point from a hand drawn curve is called vectorization (image tracing). I is a quite complex task.
I think you can get much better results by using a simple algorithm like this :
- Store all coordinate in a FIFO list
- move your sprite in direction of the next point of the list
- once the sprite is clause enough to the point discard the point and continue with next point
- Ease the movement by using simple smoothing algorithm (xSpeed, ySpeed, damping), just ask me if you need help for this
EDIT :
I just checked flight control video, I would do it like this. Once the user press on one it select it. Then user start drawing, plot point one by one as close as possible to the user finger (movements are limited by plane turning radius). This will record a chain of steps. Each step is defined by its angle (I think speed is constant), this angle must be equal to the previous one +/- turning capability.
Use simple trigonometry to compute x,y coordinates.
Look at this :
How to make a sprite point at the mouse. XNA C#
You'll find better help for that on https://gamedev.stackexchange.com/ sure someone have a ready to paste code similar to what you need. I had done this years ago in Amos on Amiga, but I could not get the code to paste it here, sorry :)