Context. The15 N isotopologue abundance ratio measured today in different bodies of the solar system is thought to be connected to 15 N-fractionation effects that would have occurred in the protosolar nebula. Aims. The present study aims at putting constraints on the degree of 15 N-fractionation that occurs during the prestellar phase, through observations of D, 13 C, and 15 N-substituted isotopologues towards B1b. Molecules both from the nitrogen hydride family, i.e. N 2 H + , and NH 3 , 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 H 2 density. These parameters were subsequently used as input in a non-local radiative transfer model to infer the radial abundance profiles of the various molecules. Results. Our modelling shows that all the molecules are affected by depletion onto dust grains in the region that encompasses the B1-bS and B1-bN cores. While high levels of deuterium fractionation are derived, we conclude that no fractionation occurs in the case of the nitrogen chemistry. Independently of the chemical family, the molecular abundances are consistent with 14 N/ 15 N ∼ 300, a value representative of the elemental atomic abundances of the parental gas. Conclusions. The inefficiency of the 15 N-fractionation effects in the B1b region can be linked to the relatively high gas temperature ∼17 K, which is representative of the innermost part of the cloud. Since this region shows signs of depletion onto dust grains, we cannot exclude the possibility that the molecules were previously enriched in 15 N, earlier in the B1b history and that such an enrichment could have been incorporated into the ice mantles. It is thus necessary to repeat this kind of study in colder sources to test such a possibility.