Quantum conductance fluctuations are investigated in disordered 3D topological insulator quantum wires. Both experiments and theory reveal a new transport regime in a mesoscopic conductor, pseudo-ballistic transport, for which ballistic properties persist beyond the transport mean free path, characteristic of diffusive transport. It results in non-universal conductance fluctuations due to quasi-1D surface modes, as observed in long and narrow Bi$_2$Se$_3$ nanoribbons. Spin helical Dirac fermions in quantum wires retain pseudo-ballistic properties over an unusually broad energy range, due to strong quantum confinement and weak momentum scattering.
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