A search is performed for narrow resonances decaying to final states of two jets, with at least one jet originating from a $b$ quark, in proton-proton collisions at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$. The data set corresponds to an integrated luminosity of $138\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the CMS detector at the LHC. Jets originating from energetic $b$ hadrons are identified through a $b$-tagging algorithm that utilizes a deep neural network or the presence of a muon inside a jet. The invariant mass spectrum of jet pairs is well described by a smooth parametrization and no evidence for the production of new particles is observed. Upper limits on the production cross section are set for excited $b$ quarks and other resonances decaying to dijet final states containing $b$ quarks. These limits exclude at 95% confidence level models of ${Z}^{\ensuremath{'}}$ bosons with masses from 1.8 TeV to 2.4 TeV and of excited $b$ quarks with masses from 1.8 TeV to 4.0 TeV. This is the most stringent exclusion of excited $b$ quarks to date.