How do you represent B-splines or Bezier Curves in C(4,1) conformal geometry? Specifically, how do you represent parallel curves or offset curves?
And how do you represent error and uncertainty about the locations and curvature of these curves at each point?

I don't know what C(4,1) conformal geometry is.
You can not represent the offset of a Bezier curve exactly as another Bezier curve, except in certain very special cases. 
You can, of course, construct a Bezier curve that is an approximation of the offset. A few ways to do this are outlined in the answers to this question. If those methods don't meet your requirements, then please tell us about your requirements, and we'll try again.
