Mediates the positive regulation of the beta-glucoside (bgl) operon by functioning as a transcriptional antiterminator. This is an RNA-binding protein that recognizes a specific sequence located just upstream of two termination sites within the operon. Phosphorylated and inactivated by BglF (eII-bgl). The degree of phosphorylation is dependent on the presence or absence of beta-glucosides which act as inducers of the operon expression. Addition of inducer result in the rapid dephosphorylation of BglG. Belongs to the transcriptional antiterminator BglG family.