Exclusive B production at CMS with the first LHC data

B physics will be one of the key physics themes at the Large Hadron Collider (LHC). In this talk, we present the estimated sensitivities of CMS for observing and measuring properties of exclusive final states $\mathrm{B \; \rightarrow \; J/\psi \; X}\ $ during the first LHC running period. Apart from probing the heavy quarks at the LHC c.m.s. energy, these measurements are also important standard candles for upcoming measurements.