Inelastic neutron scattering was used to determine the spin Hamiltonian for the singlet ground state system of fully deuterated BPCB, (C$_{5}$D$_{12}$N)$_{2}$CuBr$_{4}$. A 2-leg spin-1/2 ladder model, with $J_bot = (1.09 pm 0.01)$ meV and $J_| = (0.296 pm 0.005)$ meV, accurately describes the data. The experimental limit on the effective inter-ladder exchange constant is $|J_{rm int}^{rm eff}|lesssim 0.006$ meV, and the limit on total diagonal, intra-ladder exchange is $|J_F+J_{F}|leq 0.1$ meV. Including the effects of copper to bromide covalent spin transfer on the magnetic form-factor, the experimental ratios of intra-ladder bond energies are consistent with the predictions of continuous unitary transformation.
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