The ratios of the Bc(2S)+ to Bc+, Bc∗(2S)+ to Bc+, and Bc∗(2S)+ to Bc(2S)+ production cross sections are measured in proton-proton collisions at s=13 TeV, using a data sample collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 143 fb-1. The three measurements are made in the Bc+ meson phase space region defined by the transverse momentum pT>15 GeV and absolute rapidity |y|<2.4, with the excited Bc(∗)(2S)+ states reconstructed through the Bc(∗)+π+π-, followed by the Bc+→J/ψπ+ and J/ψ→μ+μ- decays. The Bc(2S)+ to Bc+, Bc∗(2S)+ to Bc+, and Bc∗(2S)+ to Bc(2S)+ cross section ratios, including the unknown Bc(∗)(2S)+→Bc(∗)+π+π- branching fractions, are (3.47±0.63(stat)±0.33(syst))%, (4.69±0.71(stat)±0.56(syst))%, and 1.35±0.32(stat)±0.09(syst), respectively. None of these ratios shows a significant dependence on the pT or |y| of the Bc+ meson. The normalized dipion invariant mass distributions from the decays Bc(∗)(2S)+→Bc(∗)+π+π- are also reported.