The solution to the problem of calculating the distance between an ellipse and a point is less than straightforward. The problem can be solved analytically however, which boild down to solving a quartic equation in cos(f), with (f) the true anomaly on the ellipse.
This submission implements this and computes the distances between any 3-D ellipse and an arbitrary number of 3-D points.
This is part of:
Ik-Sung Kim: "An algorithm for finding the distance between two ellipses". Commun. Korean Math. Soc. 21 (2006), No.3, pp.559-567
See also my other submission, distanceEllipseEllipse.