A search for new resonances decaying into jets containing b-hadrons in $pp$ collisions with the ATLAS detector at the LHC is presented in the dijet mass range from 0.57 TeV to 7 TeV. The dataset corresponds to an integrated luminosity of up to 36.1 fb$^{-1}$ collected in 2015 and 2016 at $\sqrt{s} = 13$ TeV. No evidence of a significant excess of events above the smooth background shape is found. Upper cross-section limits and lower limits on the corresponding signal mass parameters for several types of signal hypotheses are provided at 95% CL. In addition, 95% CL upper limits are set on the cross-sections for new processes that would produce Gaussian-shaped signals in the di-b-jet mass distributions.