Convert a B-Spline into Bezier curves

What you need is something called "Boehm's algorithm" (after its originator, Wolfgang Boehm). It has a simple geometric interpretation, and drawing a few pictures should make it clear. There is a pretty good explanation (with pictures) in this document.

The algorithm is based on a process called "knot insertion". You keep inserting knots into the b-spline curve until each knot has multiplicity 3. Then, the b-spline control points of this refined curve give you the Bezier control points of its segments.

So, if you're writing code to do this, one approach is to write a knot insertion function first, and then call it repeatedly.

There is knot insertion code here.