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Binary solid-state materials offer unique insight into how the interplay of factors such as stoichiometry and bonding interactions affects magnetism and electronic properties. We considered systems where a transition metal provides the spin moment and a heavy main group element bolsters strong spin-orbit coupling. Within this context, cobalt, a known component of permanent magnets, and bismuth, functionally the heaviest element stable to radioactive decay, form a compelling combination. The Co-Bi system has been previously shown to exhibit superconductivity in a phase recovered from high pressure. We expected the Co-Bi system could also be ferromagnetic, resulting in two sets of compounds within one chemical system, one superconducting and one ferromagnetic. Subsequently, we investigated the Co-Bi system through both experimental and theoretical approaches to discover new candidates for permanent magnets. Ab initio random structure searching calculations identified five new compounds with diverse structural motifs that may form at higher pressures than previously reported. Experimental high-pressure synthesis yielded four compounds: α-CoBi, α-CoBi, β-CoBi, and β-CoBi. Three of these phases, α-CoBi, β-CoBi, and β-CoBi, were consistent with the calculated structures, corresponding to a 60% success rate for our structure search and underscoring the strength of combining computation with experiment. Theory predicts β-CoBi and β-CoBi are ferromagnetic, with β-CoBi possessing larger magnetocrystalline anisotropy energy than familiar permanent magnets such as CoPt and Nd-Fe-B. These results suggest the Co-Bi system could be a platform for understanding the factors that underpin magnetism and, to an extent, superconductivity in a chemically simple binary system.