Background: The LHCb Collaboration has studied a number of kinematic correlations between B-hadron pairs through their subsequent decays to J/ψ pairs at 7 and 8 TeV for four minimum values of the J/ψ pT . Purpose: In this work, these measurements are compared to calculations of bb pairs and their hadronization and inclusive decays to J/ψJ/ψ are compared to the same observables. Potential cold matter effects on the bb pair observables are discussed to determine which are most likely to provide insights about the system and why. Methods: The calculations, employing the exclusive HVQMNR code, assume the same intrinsic kT -broadening and fragmentation as in Ref. [1]. The pair distributions presented by LHCb are calculated in this approach, both for the parent bb and the J/ψJ/ψ pairs produced in their decay. The sensitivity of the results to the intrinsic kT broadening is shown. The theoretical uncertainties due to the b quark mass and scale variations on both the initial bb pairs and the resulting J/ψ pairs are also shown. Possible effects due to the presence of the nucleus are studied by increasing the size of the kT broadening and modification of the fragmentation parameter. Results: Good agreement with the LHCb data is found for all observables. The parent bb distributions are more sensitive to the kT broadening than are the final-state J/ψ pairs. Conclusions: Next-to-leading order calculations with kT broadening, as in Ref.[1], can describe all correlated observables. Multiple measurements of correlated observables are sensitive to different nuclear effects which can help distinguish between them.