B-Spline patches on the tessellation shader. How to get the control points
For regular quad faces, what you want to do is send the vertices for the quad you're evaluating and the eight neighboring quads around it: a total of 4x4 vertices. The B-spline needs to know where the neighboring vertices are in order to generate a surface patch that connects smoothly to the neighboring patches.

In the case that the adjacent faces aren't quads, I don't think you can use the straightforward B-spline evaluation. In Catmull-Clark subdivision, everything is quads after the first level of subdivision, though you'll still have extraordinary vertices to deal with.