Fiducial cross-sections for t (t) over bar production with one or two additional b-jets are reported, using an integrated luminosity of 20.3 fb(-1) of proton-proton collisions at a centre-of-mass energy of 8 TeV at the Large Hadron Collider, collected with the ATLAS detector. The cross-section times branching ratio for t (t) over bar events with at least one additional b-jet is measured to be 950 +/- 70 (stat.)(-190)(+240) (syst.) fb in the lepton-plus-jets channel and 50 +/- 10 (stat.)(-10)(+15) (syst.) fb in the e mu channel. The cross-section times branching ratio for events with at least two additional b-jets is measured to be 19.3 +/- 3.5 (stat.) +/- 5.7 (syst.) fb in the dilepton channel (e mu, mu mu, and ee) using a method based on tight selection criteria, and 13.5 +/- 3.3 (stat.) +/- 3.6 (syst.) fb using a looser selection that allows the background normalisation to be extracted from data. The latter method also measures a value of 1.30 +/- 0.33 (stat.) +/- 0.28 (syst.)% for the ratio of t (t) over bar production with two additional b-jets to t (t) over bar production with any two additional jets. All measurements are in good agreement with recent theory predictions.