It looks like this paper is what you want. I think the paper gives an algorithm for generating all the minimal (under subgraph inclusion) subgraphs connecting the blue vertices (from which it is easy to obtain all such subgraphs).

It looks like the paper

Generating all the Steiner trees and computing Steiner intervals for a fixed number of terminals

by Costa Dourado, de Oliveira, and Protti is what you want (available from ScienceDirect). I think the paper gives an algorithm for generating all the minimal (under subgraph inclusion) subgraphs connecting the blue vertices (from which it is easy to obtain all such subgraphs).