  We calculate the spectrum of $B_c$ mesons using a non-relativistic quark
potential model. Using the calculated wave functions, we compute the radiative
widths of $B_c$ excited states. The strong decay widths are calculated in a
modified $^3P_0$ model, assuming harmonic oscillator wave functions. The
hadronic transition rates of $B_c$ mesons are calculated using the Kuang-Yan
approach. These results are used to determine branching ratios of possible
decay channels of several $B_c$ excited states. Calculated branching ratios are
then combined with production cross section of $B_c$ states at the LHC to
suggest strategies to find missing excited states of $B_c$ mesons.
