A structure is observed in the B +/- K -/+ mass spectrum in a sample of proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9fb-1. The structure is interpreted as the result of overlapping excited Bs0 states. With high significance, a two-peak hypothesis provides a better description of the data than a single resonance. Under this hypothesis the masses and widths of the two states, assuming they decay directly to B +/- K -/+, are determined to be m1=6063.5 +/- 1.2(stat)+/- 0.8(syst)Me,Gamma 1=26 +/- 4(stat)+/- 4(syst)Me,m2=6114 +/- 3(stat)+/- 5(syst)Me,Gamma 2=66 +/- 18(stat)+/- 21(syst)Me.Alternative values assuming a decay through B +/- K -/+, with a missing photon from the B +/- -> B +/- gamma decay, which are shifted by approximately 45MeV, are also determined. The possibility of a single state decaying in both channels is also considered. The ratio of the total production cross-section times branching fraction of the new states relative to the previously observed Bs20 state is determined to be 0.87 +/- 0.15(stat)+/- 0.19(syst).