It sounds like you want to determine whether an mRNA is being expressed from a beta-globin gene in E. coli. One approach is to look for a beta-globin sequence in the total mRNA expressed by the bacterium. Here are two techniques that could be useful:
MrMistery asked whether the beta-hemoglobin gene was cloned into E. coli. If so, that can simplify the problem. If the gene is inserted into a plasmid vector in the E. coli, you could do a plasmid prep and so produce a less complex population of nucleic acid to probe or sequence.
