Using the full CDF Run II data sample, we report evidence for a new resonance, which we refer to as B(5970), found simultaneously in the B0π+ and B+ π− mass distributions with a significance of 4.4 standard deviations. We further report the first study of resonances consistent with orbitally excited B+ mesons and an updated measurement of the properties of orbitally excited B0 and Bs0 mesons. We measure the masses and widths of all states, as well as the relative production rates of the B1 , B2*, and B(5970) states and the branching fraction of the Bs2*0 state to either B*+ K − and B+ K− Furthermore, we measure the production rates of the orbitally excited B0,+ states relative to the B0,+ ground state. The masses of the new B(5970) resonances are 5978 ± 5(stat) ± 12(syst) MeV/c2 for the neutral state and 5961 ± 5(stat) ± 12(syst) MeV/c2 for the charged state, assuming that the resonance decays into Bπ final states. The properties of the orbitally excited and the new B(5970)0,+ states are compatible with isospin symmetry.