The interaction and propagation of anti-B mesons with light mesons, N and Delta baryons is studied within a unitarized approach based on effective models that are compatible with chiral and heavy-quark symmetries. We find several heavy-quark spin doublets in the open-bottom sectors, where anti-B and anti-B* mesons are present. In the meson sector we find several resonant states, among them, a B0 and a B1 with masses 5530 MeV and 5579 MeV as well as Bs0* and Bs1* narrow states at 5748 MeV and 5799 MeV, respectively. They form two doublets with no experimental identification yet, the first one being the bottom counterpart of the D0(2400) and D1(2430) states, and the second bottom doublet associated to the ubiquitous Ds0* (2317) and the Ds1 (2460). In the baryon sector, several Lambda_b and Sigma_b doublets are identified, among them the one given by the experimental Lambda_b(5910) and Lambda*_b(5921). Moreover, one of our states, the Sigma_b*(5904), turns out to be the bottom counterpart of the Sigma*(1670) and Sigma_c*(2549), which is a case for discovery. We finally analyze different transport coefficients for the anti-B meson in hot matter, such as formed in heavy-ion collisions at RHIC and LHC. For RHIC/LHC energies, the main contribution to the coefficients comes from the interaction of anti-B mesons with pions. However, we also include the effects of baryonic density which might be sizable at temperatures T < 100 MeV, as the chemical potential is expected to increase in the last stages of the expansion. We conclude that although the relaxation time decreases with larger baryonic densities, the anti-B meson does not thermalize at RHIC/LHC energies, representing an ideal probe for the initial bottom distribution.