The high index (441) surface of bismuth has been studied using Scanning Tunnelling Microscopy (STM), Angle Resolved Photoemission Spectroscopy (APRES) and spin-resolved ARPES. The surface is strongly corrugated, exposing a regular array of (110)-like terraces. Two surface localised states are observed, both of which are linearly dispersing in one in-plane direction ($k_x$), and dispersionless in the orthogonal in-plane direction ($k_y$), and both of which have a Dirac-like crossing at $k_x$=0. Spin ARPES reveals a strong in-plane polarisation, consistent with Rashba-like spin-orbit coupling. One state has a strong out-of-plane spin component, which matches with the miscut angle, suggesting its {possible} origin as an edge-state. The electronic structure of Bi(441) has significant similarities with topological insulator surface states and is expected to support one dimensional Quantum Spin Hall-like coupled spin-charge transport properties with inhibited backscattering, without requiring a topological insulator bulk.