Supersymmetric theories with bilinear $R$-parity violation can give rise to the observed neutrino masses and mixings. One important feature of such models is that the lightest supersymmetric particle might have a sufficiently large lifetime to produce detached vertices. Working in the framework of supergravity models, we analyze the potential of the LHCb experiment to search for supersymmetric models exhibiting bilinear $R$-parity violation. We show that the LHCb experiment can probe a large fraction of the ${m}_{0}\ensuremath{\bigotimes}{m}_{1/2}$, being able to explore gluino masses up to 1.3 TeV. The LHCb discover potential for these kinds of models is similar to the ATLAS and CMS ones in the low luminosity phase of operation of the LHC.