  We report temperature-dependent neutron scattering measurements of the local
dynamic structure factor in the quantum spin ladder
(C$_{7}$H$_{10}$N)$_{2}$CuBr$_{4}$ in a magnetic field $H=9$~T, in its gapless
quantum-critical phase. We show that the measured quantity has a scaling form
consistent with expectations for a Tomonaga-Luttinger liquid with attraction.
The measured Luttinger parameter $K\approx1.25$ and scaling function are in
excellent agreement with density matrix renormalization group numerical
calculations for the underlying spin Hamiltonian.
