Context. The 15N isotopologue abundance ratio measured today in different bodies of the solar system is thought to be connected to 15N-fractionation effects that would have occurred in the protosolar nebula. Aims. The present study aims at putting constraints on the degree of 15N-fractionation that occurs during the prestellar phase, through observations of D, 13C, and 15N-substituted isotopologues towards B1b. Molecules both from the nitrogen hydride family, i.e. N2H+, and NH3, and from the nitrile family, i.e. HCN, HNC, and CN, are considered in the analysis. Methods. As a first step, we modelled the continuum emission in order to derive the physical structure of the cloud, i.e. gas temperature and H2 density. These parame...