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).