We employ an ab-initio structure search algorithm to explore the configurational space of bismuth in quasi-two dimensions. A confinement potential is introduced to restrict the movement of atoms within a predefined thickness to find the stable and metastable forms of monolayer Bi. In addition to the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new phases: α, β, and γ. Each phase exhibits peculiar electronic properties, ranging from metallic (α and γ) to semiconducting (puckered monoclinic, buckled hexagonal, and β) monolayers. Topologically nontrivial features are predicted for buckled hexagonal and γ phases. We also remark on the role of 5d electrons on the electronic properties of Bi monolayer. We conclude that Bi provides a rich playground to study distortion-mediated metal-insulator phase transitions in quasi-2D.