We study the impact of contact interactions involving two leptons (electrons or muons) and two b-quarks (bb¯ℓ+ℓ−) on the high-mass di-lepton region at the LHC. We consider different selections of b-tagged jet multiplicities in the di-lepton final states: inclusive (no selection), 0, 1 and 2 b-tagged jets, and show that the single b-jet selection significantly improves the sensitivity to New Physics (NP) in the form of the bb¯ℓ+ℓ− contact term. We obtain a better sensitivity compared to the currently existing searches of NP in the di-lepton inclusive channel. In particular, the expected limits go beyond competitive bounds set by LEP (for electrons) on the scale of NP, Λ, by a factor of 1.2−3.1, depending on the chirality structure of the operator. In addition, the expected limits on Λ, set by using a non-resonant LHC di-lepton inclusive search, are expected to be improved by a factor of 1.3−1.4 for both electrons and muons.