We substantially refine our previously developed model for the suppression of Upsilon mesons in the quark-gluon plasma (QGP) formed in 2.76 TeV PbPb collisions at the LHC. It accounts for gluodissociation of the six bottomium states Y(nS), chi_b(nP) with n = 1,2,3, collisional damping of these states as described in a complex potential, screening of the real part of the potential, and the subsequent decay cascade. In the hydrodynamical calculation of the expanding fireball, we take into account the effect of transverse expansion on the suppression factors, and finite transverse momenta of the heavy mesons in the medium. The running of the coupling is considered, resulting in larger gluodissociation decay widths. The initial central temperature is found to be 550 MeV at 0.1 fm/c. Our results are in good agreement with recent centrality-dependent CMS and ALICE data. The calculated suppression of the excited states relative to the ground state Y(1S) is not strong enough in peripheral collisions. Additional mechanisms are discussed. Predictions for 5.52 TeV are made.