Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the Bq (q=n,s) mesons are shown to be in full agreement with experiment if a universal coupling αHF = 0.310 is taken in perturbative spin-spin potential. It gives M (B * ) − M (B) = 45.7(3) MeV, M (B * s ) − M (Bs) = 46.7(3) MeV (n f = 4), while in bottomonium ∆HF (bb) = M (Υ(9460)) − M (η b (1S)) = 63.4 MeV for n f = 4 and 71.1 MeV for n f = 5 are obtained; just latter agrees with recent BaBar data. For unobserved excited states we predict M (Υ(2S)) − M (η b (2S)) = 36(2) MeV, M (Υ(3S)) − M (η(3S)) = 28(2) MeV, and also M (B * c ) = 6334(4) MeV, M (Bc(2S)) = 6868(4) MeV, M (B * c (2S)) = 6905 (4) MeV. The mass splittings between D(2 3 S1) − D(2 1 S0), Ds(2 3 S1) − Ds(2 1 S0) are predicted to be ∼ 70 MeV, which are significantly smaller than in several other studies. * Electronic address: badalian@itep.ru † Electronic address: blg.bakker@few.vu.nl ‡ Electronic address: danilkin@itep.ru