Answers for "moving linearly along a bezier curve"
http://answers.unity.com/questions/1162684/moving-linearly-along-a-bezier-curve.html
The latest answers for the question "moving linearly along a bezier curve"Answer by Eno-Khaon
http://answers.unity.com/answers/1162703/view.html
You're on the right track.
To take a note from [a great source on Bezier curve information][1],
> there is no generic formula that
> allows you to calculate the arc
> length.
With this in mind, a good enough approach is to break down the curve into points, whether at roughly-equidistant or arbitrary lengths, then interpolate between the nearest points on each side of your target.
Unfortunately, there is no inexpensive, perfect solution to this problem, but if perfection isn't absolutely necessary, you can still get indistinguishably close through quicker calculations than you might expect.
[1]: http://pomax.github.io/bezierinfo/Tue, 29 Mar 2016 17:05:17 GMTEno-Khaon