Emergent excitations known as Majorana modes could be a platform for decoherence-resistant quantum computing. These Majorana modes are predicted to exist the boundaries of topological superconductors: materials with topological surface states and p-wave electron pairing. Layered superconductor β-PdBi2 satisfies the first criterion, with some evidence for a p-wave pairing component in thin films and at the surface under certain conditions. We have developed a tight binding model, from which we derive a continuum model to describe bulk and surface states in β-PdBi2. Using a self-consistent theoretical framework, we identify a magnetic field-induced first order phase transition between s- and effective p-wave states in a spin-helical Fermi surface resembling that of β-PdBi₂. We discuss the origin of this effect due to the interplay of spin-orbit coupling and magnetic fields, before extending our analysis to more closely describe surface contributions to superconductivity in β-PdBi₂.